Dynamical Systems: Theory and Applications

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.3	2011	18.4 Days	CHF 2400
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600
Vibration vibration	1.9	3.2	2018	29.3 Days	CHF 1600
Symmetry symmetry	2.2	5.4	2009	17.3 Days	CHF 2400
Materials materials	3.1	5.8	2008	13.9 Days	CHF 2600

16 pages, 670 KiB

Open AccessFeature PaperArticle

Multi-Objective LQG Design with Primal-Dual Method

by Donghwan Lee

Mathematics 2023, 11(8), 1857; https://doi.org/10.3390/math11081857 - 13 Apr 2023

Cited by 3 | Viewed by 2001

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To [...] Read more.

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To tackle this problem, we propose an efficient bisection line search algorithm that outperforms other approaches such as semidefinite programming in terms of computational efficiency. The primary idea behind our algorithm is to use the Lagrangian function and Karush–Kuhn–Tucker (KKT) optimality conditions to address the constrained optimization problem. The bisection line search is employed to search for the Lagrange multiplier. Furthermore, we provide numerical examples to illustrate the efficacy of our proposed methods. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 2879 KiB

Open AccessArticle

The Highly Accurate Interatomic Potential of CsPbBr₃ Perovskite with Temperature Dependence on the Structure and Thermal Properties

by Qianyu You, Shun Gu and Xiaofan Gou

Materials 2023, 16(5), 2043; https://doi.org/10.3390/ma16052043 - 1 Mar 2023

Cited by 6 | Viewed by 3342

Abstract

CsPbBr₃ perovskite has excellent optoelectronic properties and many important application prospects in solar cells, photodetectors, high-energy radiation detectors and other fields. For this kind of perovskite structure, to theoretically predict its macroscopic properties through molecular dynamic (MD) simulations, a highly accurate interatomic [...] Read more.

CsPbBr₃ perovskite has excellent optoelectronic properties and many important application prospects in solar cells, photodetectors, high-energy radiation detectors and other fields. For this kind of perovskite structure, to theoretically predict its macroscopic properties through molecular dynamic (MD) simulations, a highly accurate interatomic potential is first necessary. In this article, a new classical interatomic potential for CsPbBr₃ was developed within the framework of the bond-valence (BV) theory. The optimized parameters of the BV model were calculated through first-principle and intelligent optimization algorithms. Calculated lattice parameters and elastic constants for the isobaric–isothermal ensemble (NPT) by our model are in accordance with the experimental data within a reasonable error and have a higher accuracy than the traditional Born–Mayer (BM) model. In our potential model, the temperature dependence of CsPbBr₃ structural properties, such as radial distribution functions and interatomic bond lengths, was calculated. Moreover, the temperature-driven phase transition was found, and the phase transition temperature was close to the experimental value. The thermal conductivities of different crystal phases were further calculated, which agreed with the experimental data. All these comparative studies proved that the proposed atomic bond potential is highly accurate, and thus, by using this interatomic potential, the structural stability and mechanical and thermal properties of pure inorganic halide and mixed halide perovskites can be effectively predicted. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 915 KiB

Open AccessArticle

Finite-Time Bounded Tracking Control for a Class of Neutral Systems

by Jiang Wu, Yujie Xu, Hao Xie and Yao Zou

Mathematics 2023, 11(5), 1199; https://doi.org/10.3390/math11051199 - 28 Feb 2023

Cited by 1 | Viewed by 1327

Abstract

In this paper, we investigate finite-time bounded (FTB) tracking control for a class of neutral systems. Firstly, the dynamic equation of the tracking error signal is given based on the original neutral system. Then, we combine it with the equations of the state [...] Read more.

In this paper, we investigate finite-time bounded (FTB) tracking control for a class of neutral systems. Firstly, the dynamic equation of the tracking error signal is given based on the original neutral system. Then, we combine it with the equations of the state vector to construct an error system, where the reference signal and the disturbance signal are fused in a new vector. Next, about the error system, we study the input–output finite-time stability problem of the closed-loop system by utilizing the Lyapunov–Krasovskii functional. We also give a finite-time stability condition in the form of linear matrix inequalities (LMIs). Furthermore, the delay-dependent and delay-independent finite-time bounded tracking controllers are designed separately for the original system. Finally, a realistic example is given to show the effectiveness of the controller design method in the paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 10607 KiB

Open AccessArticle

Dynamic Behavior Analysis of I-Shaped RC Beams under Combined Blast and Impact Loads

by Jianyu Liu, Yiping Yin, Yunlei Zhao and Yuan Li

Appl. Sci. 2023, 13(3), 1943; https://doi.org/10.3390/app13031943 - 2 Feb 2023

Cited by 1 | Viewed by 2699

Abstract

The existing literature mainly focuses on the research of reinforced concrete (RC) beams under a single load such as blast or impact. In this paper, the slab–rib–slab RC beam, a new type of structure widely used in bridge structures, was taken as the [...] Read more.

The existing literature mainly focuses on the research of reinforced concrete (RC) beams under a single load such as blast or impact. In this paper, the slab–rib–slab RC beam, a new type of structure widely used in bridge structures, was taken as the research object. The explicit dynamic analysis software LS-DYNA was used to numerically analyze the dynamic response and failure behavior of I-shaped RC beams under combined blast and impact loads. For this reason, an effective numerical analysis model was obtained by carrying out experiments on I-shaped RC beams under contact explosion. The key factors affecting the dynamic response of the structure under combined loads were numerically analyzed. Numerical results showed that different load application sequences have important effects on the dynamic response of the structure. When the impact load was first applied to the structure, more severe concrete damage and deformation occured in the depth direction of the beam. However, when the blast load was first applied to the structure, the concrete at the lower flange was damaged in the span direction of the beam due to tension, and no large-scale concrete spallation occurred in the depth direction. This was mainly due to the different mechanisms of blast and impact loads. In addition, the vulnerability of the I-shaped RC beams varied with some structural parameters, including span, depth, and configuration of reinforcement. At the same time, the results showed that the structure is more sensitive to changes in structural parameters when it is first subjected to impact loads. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 643 KiB

Open AccessArticle

Compound-Combination Synchronization for Fractional Hyperchaotic Models with Different Orders

by Gamal M. Mahmoud, Asma Althemairi, Tarek M. Abed-Elhameed and Ahmed A. Farghaly

Symmetry 2023, 15(2), 279; https://doi.org/10.3390/sym15020279 - 19 Jan 2023

Cited by 4 | Viewed by 1308

Abstract

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described [...] Read more.

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described and proved. We introduce, also, the FO hyperchaotic complex Lü, Chen, and Lorenz models with complex periodic forcing. The symmetry property is found in the FO hyperchaotic complex Lü, Chen, and Lorenz models. These hyperchaotic models are found in many areas of applied sciences, such as physics and secure communication. These FO hyperchaotic models are used as an example for our proposed synchronization. The numerical simulations show a good agreement with the analytical results. The complexity and existence of additional variables mean that it is safer and interesting to transmit and receive signals in communication theory. The proposed scheme of synchronization is considered a generalization of many types in the literature and other examples can be found in similar studies. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

23 pages, 1240 KiB

Open AccessArticle

Observer-Based PID Control Protocol of Positive Multi-Agent Systems

by Xiaogang Yang, Mengxing Huang, Yuanyuan Wu and Siling Feng

Mathematics 2023, 11(2), 419; https://doi.org/10.3390/math11020419 - 12 Jan 2023

Cited by 10 | Viewed by 2727

Abstract

This paper proposes the observer-based proportional-integral-derivative control of positive multi-agent systems. First, a positive observer is constructed for the considered multi-agent systems in terms of a matrix decomposition approach. Then, a novel proportional-integral-derivative protocol framework is proposed based on an improved observer. By [...] Read more.

This paper proposes the observer-based proportional-integral-derivative control of positive multi-agent systems. First, a positive observer is constructed for the considered multi-agent systems in terms of a matrix decomposition approach. Then, a novel proportional-integral-derivative protocol framework is proposed based on an improved observer. By using copositive Lyapunov function, the positivity and consensus of the multi-agent systems are achieved. The corresponding observer and control protocol gain matrices are designed in terms of linear programming. Moreover, the proposed design is developed for heterogeneous positive multi-agent systems. The main contributions of this paper include the following: (i) A positive observer is constructed to estimate the states of positive multi-agent systems; (ii) A novel observer-based proportional-integral-derivative protocol is designed to handle the consensus problem of positive multi-agent systems; and (iii) The presented conditions are solvable in terms of linear programming and the gain matrices can be constructed based on a matrix decomposition technology. Finally, two illustrative examples are provided to verify the effectiveness of the design. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

23 pages, 1850 KiB

Open AccessArticle

Constrained Nonsingular Terminal Sliding Mode Attitude Control for Spacecraft: A Funnel Control Approach

by Nguyen Xuan-Mung, Mehdi Golestani and Sung Kyung Hong

Mathematics 2023, 11(1), 247; https://doi.org/10.3390/math11010247 - 3 Jan 2023

Cited by 8 | Viewed by 2359

Abstract

This paper presents an adaptive constrained attitude control for uncertain spacecraft. Inspired by the concept of nonsingular terminal sliding mode control and funnel control for nonlinear systems, a novel adaptive attitude control is introduced which contains a time-varying gain to handle the constraints [...] Read more.

This paper presents an adaptive constrained attitude control for uncertain spacecraft. Inspired by the concept of nonsingular terminal sliding mode control and funnel control for nonlinear systems, a novel adaptive attitude control is introduced which contains a time-varying gain to handle the constraints imposed on the spacecraft attitude. Indeed, when the attitude trajectory approaches the boundary of the constraint set, the control effort as well as the time-varying gain will increase in order to preclude the trajectory from intersecting the boundary. Then, it is analytically proved that the system trajectories converge to an arbitrary small region around the origin within a fixed time where the smallest upper bound of the convergence time is determined as an independent parameter in the controller. Further, the proposed control scheme is nonsingular without having to use any piecewise continuous function which simplifies stability analysis. These properties distinguish the proposed control scheme from the existing finite/fixed-time attitude controls. Finally, several simulation results confirm the robustness and performance of the proposed control framework. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 5267 KiB

Open AccessArticle

Adaptive Fuzzy Command Filtered Finite-Time Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Unknown Input Saturation and Unknown Control Directions

by Xiongfeng Deng, Yiqing Huang and Lisheng Wei

Mathematics 2022, 10(24), 4656; https://doi.org/10.3390/math10244656 - 8 Dec 2022

Cited by 6 | Viewed by 1582

Abstract

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. [...] Read more.

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 650 KiB

Open AccessArticle

Tolerance Modelling of Vibrations of a Sandwich Plate with Honeycomb Core

by Jakub Marczak

Materials 2022, 15(21), 7611; https://doi.org/10.3390/ma15217611 - 29 Oct 2022

Cited by 2 | Viewed by 1493

Abstract

Sandwich structures are commonly used in many branches of modern engineering, such as aerospace or naval constructions. In this work, a vibration analysis of such structures is performed with the use of an anlytical model based on a zig-zag hypothesis. Due to the [...] Read more.

Sandwich structures are commonly used in many branches of modern engineering, such as aerospace or naval constructions. In this work, a vibration analysis of such structures is performed with the use of an anlytical model based on a zig-zag hypothesis. Due to the assumed periodic microstructure, which may occure in any layer of the structure, the initial governing equations describing its dynamic behaviour may contain periodic, non-continuous coefficients. The main aim of the presented paper is to show an analytical solution to the issue of the vibration analysis of the mentioned structures. With the use of the tolerance averaging technique, the initial governing equations are transformed to the form with constant coefficients, which is convenient to solve using well-known mathematical methods. The derived model is a versatile solution for any type of periodically inhomogeneous sandwich plate, including sandwich plates with a honeycomb core. Eventually, in the calculation example, the application of the derived averaged model in the analysis of vibrations of such structures is presented and discussed. The convergence of results of the tolerance model and FEM analysis proves the correctness and superiority of the proposed solution. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 459 KiB

Open AccessArticle

On the Dynamics of New 4D and 6D Hyperchaotic Systems

by Samia Rezzag and Fuchen Zhang

Mathematics 2022, 10(19), 3668; https://doi.org/10.3390/math10193668 - 6 Oct 2022

Cited by 4 | Viewed by 1921

Abstract

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the [...] Read more.

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

28 pages, 8684 KiB

Open AccessArticle

Design and Development of a Mathematical Model for an Industrial Process, in a System Dynamics Environment

by Jorge Manuel Barrios Sánchez, Roberto Baeza Serrato and Marco Bianchetti

Appl. Sci. 2022, 12(19), 9855; https://doi.org/10.3390/app12199855 - 30 Sep 2022

Cited by 3 | Viewed by 3702

Abstract

This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency [...] Read more.

This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency domain based on the Laplace transform. The conventional control engineering technique is used to present and reduce the dynamic system in a block diagram as a mechanism for determining the structure of the system. The direct path equation and the feedback equation are determined to obtain mathematical models that explain the trajectory of the behavior of each state variable through a transfer function in response to the different inputs of the system. The research proposal is based on presenting an alternative of analytical validation for more robust decision-making to systems dynamics models, based on the explanation of the system structure through a transfer function and its analysis of stability and external controllability for the system dynamics model under study. The results are visually analyzed in a root diagram. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 4984 KiB

Open AccessArticle

Estimation of Resonance Frequency for Systems with Contact Using Linear Dynamics Methods

by Maciej Wnuk and Artur Iluk

Appl. Sci. 2022, 12(18), 9344; https://doi.org/10.3390/app12189344 - 18 Sep 2022

Cited by 3 | Viewed by 2576

Abstract

Limitations in determining the resonance frequency for large models, taking into account non-linearity in the form of contact, initiated work on the creation of a simplified method of estimating these resonance frequencies. The trend in this field is the use of time-domain methods [...] Read more.

Limitations in determining the resonance frequency for large models, taking into account non-linearity in the form of contact, initiated work on the creation of a simplified method of estimating these resonance frequencies. The trend in this field is the use of time-domain methods with full contact, or frequency-domain methods which take into account nonlinearity for specific cases. For simplification, classical modal analysis is often used, with boundary conditions taken into account or freeform vibrations, with neglected contact, or with tied contact areas, as though the contact was always closed. The presented approximation method is based on both types of such analysis and compensates for the error of both of the solutions. The method was elaborated with nonlinear dynamics simulations in the time domain. This work presents experimental verification of the method for a simple beam, and for more complex geometry—the satellite antenna panel. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 7510 KiB

Open AccessArticle

On the Efficiency Enhancement of an Actively Tunable MEMS Energy Harvesting Device

by Mortaza Aliasghary, Saber Azizi, Hadi Madinei and Hamed Haddad Khodaparast

Vibration 2022, 5(3), 603-612; https://doi.org/10.3390/vibration5030035 - 6 Sep 2022

Cited by 4 | Viewed by 2494

Abstract

In this paper, we propose an active control method to adjust the resonance frequency of a capacitive energy harvester. To this end, the resonance frequency of the harvester is tuned using an electrostatic force, which is actively controlled by a voltage source. The [...] Read more.

In this paper, we propose an active control method to adjust the resonance frequency of a capacitive energy harvester. To this end, the resonance frequency of the harvester is tuned using an electrostatic force, which is actively controlled by a voltage source. The spring softening effect of the electrostatic force is used to accommodate the dominant frequency of the ambient mechanical vibration within the bandwidth of the resonance region. A single degree of freedom is considered, and the nonlinear equation of motion is numerically integrated over time. Using a conventional proportional–integral–derivative (PID) control mechanism, the results demonstrated that our controller could shift the resonance frequency leftward on the frequency domain and, as a result, improve the efficiency of the energy harvester, provided that the excitation frequency is lower than the resonance frequency of the energy harvester. Application of the PID controller in the resonance zone resulted in pull-in instability, adversely affecting the harvester’s performance. To tackle this problem, we embedded a saturation mechanism in the path of the control signal to prevent a sudden change in motion amplitude. Outside the pull-in band, the saturation of the control signal resulted in the reduction of harvested power compared to the non-saturated signal; this is a promising improvement in the design and analysis of energy harvesting devices. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 2493 KiB

Open AccessArticle

Parametric Instability of Functionally Graded Porous Cylindrical Panels under the Effect of Static and Time-Dependent Axial Loads

by Salah M. Zaidan and Hamad M. Hasan

Vibration 2022, 5(3), 570-584; https://doi.org/10.3390/vibration5030033 - 2 Sep 2022

Cited by 3 | Viewed by 2025

Abstract

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear [...] Read more.

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

9 pages, 1229 KiB

Open AccessArticle

Highly Efficient Numerical Integrator for the Circular Restricted Three-Body Problem

by Xiongbiao Tu, Qiao Wang and Yifa Tang

Symmetry 2022, 14(9), 1769; https://doi.org/10.3390/sym14091769 - 25 Aug 2022

Cited by 1 | Viewed by 2081

Abstract

The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such [...] Read more.

The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such an integrator is more efficient than the symplectic Euler method and the Gauss Runge–Kutta method as regards this problem. In addition, we proved the integrator is symplectic by the discrete Hamilton’s principle. Several groups of numerical experiments demonstrated the precision and high efficiency of the integrator in the examples of the quadratic potential and the bounded orbits in the circular restricted three-body problem. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 4086 KiB

Open AccessArticle

Adaptive Fuzzy Tracking Control of Uncertain Nonlinear Multi-Agent Systems with Unknown Control Directions and a Dead-Zone Fault

by Xiongfeng Deng and Xiyu Zhang

Mathematics 2022, 10(15), 2655; https://doi.org/10.3390/math10152655 - 28 Jul 2022

Cited by 7 | Viewed by 2081

Abstract

In this paper, a class of uncertain nonlinear multi-agent systems with unknown control directions and a dead-zone fault is addressed, where unknown control gains exist in each subsystem. In terms of the approximation characteristic of a fuzzy logic system, it is used to [...] Read more.

In this paper, a class of uncertain nonlinear multi-agent systems with unknown control directions and a dead-zone fault is addressed, where unknown control gains exist in each subsystem. In terms of the approximation characteristic of a fuzzy logic system, it is used to approximate uncertain nonlinear dynamics, and then the relevant adaptive control laws are designed. Considering the presence of unknown control directions and a dead-zone fault, the Nussbaum gain function technique is introduced to design the intermediate control law and the adaptive fuzzy control law. A theoretical analysis shows that the tracking control problem of the given multi-agent systems can be effectively solved through the application of the proposed adaptive fuzzy control law and the tracking errors can converge to a small neighborhood of zero through an adjustment of the relevant parameters. Finally, the effectiveness of the theoretical analysis results is verified by two simulation cases. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 24852 KiB

Open AccessArticle

Analysis of the Influence of a Powertrain Mounting System on a Dual-Clutch Transmission Vehicle under Typical Working Conditions

by Zheng Guo, Datong Qin, Antai Li, Jihao Feng and Yonggang Liu

Appl. Sci. 2022, 12(15), 7439; https://doi.org/10.3390/app12157439 - 25 Jul 2022

Cited by 3 | Viewed by 2287

Abstract

The unsuitably designed powertrain mount may cause jittering and shrugging during the starting and shifting processes of the vehicle, which seriously affects the comfort of using the vehicle. However, the influence of mounts on vehicles has been neglected in previous studies. In view [...] Read more.

The unsuitably designed powertrain mount may cause jittering and shrugging during the starting and shifting processes of the vehicle, which seriously affects the comfort of using the vehicle. However, the influence of mounts on vehicles has been neglected in previous studies. In view of the above problems, this study establishes a DCT vehicle coupling dynamic model, considering six degrees of freedom of the powertrain mount and the engine dynamic torque, nonlinear characteristics of a dual-mass flywheel, time-varying stiffness of gear systems, and other factors. Furthermore, the effect of mounts on the longitudinal dynamic characteristics of the vehicle is studied during the starting, shifting, and tip-in/tip-out process. The results show that under typical working conditions, the mount and its stiffness and damping affect the fluctuation frequency and amplitude of the jerk. When the torque of the vehicle transmission system changes greatly, such as under starting and tip-in/tip-out conditions, the mount has a great impact on the dynamic performance of the vehicle. Simultaneously, the engine torque fluctuation can act on the vehicle through the mount, which has an impact on the jerk of the vehicle. A comparison with vehicle test results reveals that the DCT coupling dynamic model can reflect the law of the effect of the mount on the vehicle performance and verify the rationality of the model. Under typical working conditions, when the influence of the mount is not considered in the vehicle dynamic’s modeling, there is a large error of the jerk between the simulation results and the actual situation. The results provide a reference for optimizing the parameters of the mount and improving the dynamic characteristics of DCT vehicles. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 2324 KiB

Open AccessArticle

Exact Traveling Wave Solutions in a Generalized Harry Dym Type Equation

by Rong Wu and Yan Zhou

Symmetry 2022, 14(7), 1480; https://doi.org/10.3390/sym14071480 - 20 Jul 2022

Cited by 3 | Viewed by 2098

Abstract

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions [...] Read more.

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions in parameter space are examined. It is demonstrated that solitary wave solutions, periodic peakons, pseudo-peakons, and compacton solutions exist. All conceivable exact explicit parametric representations of various solutions are presented. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 3590 KiB

Open AccessArticle

Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

by Zhao Feng, Changxiang Yan, Yanfeng Qiao, Anlin Xu and Haihong Wang

Appl. Sci. 2022, 12(14), 6966; https://doi.org/10.3390/app12146966 - 9 Jul 2022

Cited by 2 | Viewed by 1903

Abstract

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the [...] Read more.

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the surveillance capability of systems that use optics as the main means for surveilling different areas of space. In this paper, the initial orbit is calculated based on the unit vector method (UVM); the geometric dilution of precision (GDOP)—derived under the condition that the approximate Lagrangian coefficient and distance are constant—is used as the parameter for the uncertainty distribution of the target orbit solution. A suitable coordinate system transformation is conducted and all possible observation geometry relationships between the target and the sensor are expressed in terms of the angle between orbital planes and the right ascension of the target and sensor in the transformed coordinate system. Simulation experiments show that the GDOP is approximately equal to that obtained statistically through Monte Carlo simulation experiments. The accuracy of the initial orbit solution is poor when the target and optical sensor are at the same right ascension and declination, or in the same orbital plane. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 4209 KiB

Open AccessArticle

A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

by Bo-Lang Zhang, Kai-Sheng Chen, Xing Hu and Kun Zhang

Appl. Sci. 2022, 12(13), 6416; https://doi.org/10.3390/app12136416 - 24 Jun 2022

Cited by 4 | Viewed by 1881

Abstract

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was [...] Read more.

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was separated into static and alternating load in accordance with cyclic load characteristics, and the strain of clay under static and alternating load was analyzed. Then, on the basis of the variable-order Abel dashpot model, rheological theory and elastoplastic theory, the expressions of the rheological constitutive model and strain response were both obtained. Finally, in combination with the undrained dynamic triaxial testing of Zhan Jiang clay and Tian Jin soft clay, a series of analyses was carried out on the effectiveness and parameter sensitivity of the model when subjected to long-term cyclic loading. By comparing the dynamic constitutive model with pre-existing models, the superiority of the dynamic constitutive model is revealed. The results show that the dynamic constitutive model can characterize properly the deformation characteristics of clay under the action of long-term cyclic loading, especially in its accelerating stage. The parameter sensitivity of the model exhibits a growing trend with the increment of loading duration. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

25 pages, 14122 KiB

Open AccessArticle

Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting

by Miao Yuan, Youzuo Jin, Kefu Liu and Ayan Sadhu

Vibration 2022, 5(3), 383-407; https://doi.org/10.3390/vibration5030022 - 22 Jun 2022

Cited by 2 | Viewed by 2613

Abstract

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used [...] Read more.

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used as a tunable absorber damper. This non-traditional vibration absorber is attached to a primary system that is subjected to random base excitation. An analytical study is conducted by assuming that the base excitation is white noise. In terms of vibration suppression, the objective of the optimization is to minimize the power dissipated by the primary damper and maximize the power dissipated by the absorber damper. It is found that when the primary system is undamped, the power dissipated by the absorber damper remains a constant that is related to the mass ratio. The higher the mass ratio, the higher the power dissipated. When the primary system is damped, the minimization of the power dissipated by the primary damping is equivalent to the maximization of the power dissipated by the absorber damper. The existence of the optimum solutions depends on both the mass ratio and the primary damping ratio. In terms of energy harvesting, the objective of optimization is to maximize the power harvested by the load resistor. It is found that for a given mass ratio and primary damping ratio, the optimum frequency tuning ratio required to maximize vibration suppression is slightly higher than that required to maximize the harvested power. The trade-off issue between vibration suppression and energy harvesting is investigated. An apparatus is developed to allow frequency tuning and damping tuning. Both the numerical simulation and experimental study with band-limited white noise validate the general trends revealed in the analytical study. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 12924 KiB

Open AccessArticle

Harmonic Balance Method to Analyze the Steady-State Response of a Controlled Mass-Damper-Spring Model

by Ali Kandil, Y. S. Hamed and Jan Awrejcewicz

Symmetry 2022, 14(6), 1247; https://doi.org/10.3390/sym14061247 - 16 Jun 2022

Cited by 9 | Viewed by 3475

Abstract

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) [...] Read more.

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA), were applied to suppress the undesired oscillations of the harmonically-excited car. 2D and 3D graphical plots are included based upon the equations resulting from the harmonic balance method. Moreover, a numerical simulation was established using the fourth order Rung–Kutta technique in order to confirm the overall controlled behavior of the studied model. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 244 KiB

Open AccessArticle

Continued Fraction Expansions of Stable Discrete-Time Systems of Difference Equations

by Ziad Zahreddine

Symmetry 2022, 14(6), 1226; https://doi.org/10.3390/sym14061226 - 13 Jun 2022

Cited by 1 | Viewed by 1802

Abstract

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the procedure, and we provide an application on [...] Read more.

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the procedure, and we provide an application on the stability of two-dimensional digital filters. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

12 pages, 3692 KiB

Open AccessArticle

Efficiency Analysis of Herringbone Star Gear Train Transmission with Different Load-Sharing Conditions

by Dong Li, Shuyan Wang, Dongliang Li and Yong Yang

Appl. Sci. 2022, 12(12), 5970; https://doi.org/10.3390/app12125970 - 11 Jun 2022

Cited by 4 | Viewed by 2384

Abstract

A slight improvement in the transmission efficiency of the herringbone star gear train in a GTF has a great impact on the fuel economy of the engine. Here, the influencing factors of gear train efficiency were studied from the perspective of gear train [...] Read more.

A slight improvement in the transmission efficiency of the herringbone star gear train in a GTF has a great impact on the fuel economy of the engine. Here, the influencing factors of gear train efficiency were studied from the perspective of gear train composition, and the efficiency calculation model of the split star gear train, including the load-sharing coefficient, was established. Based on the efficiency calculation model, the mechanical relationship affecting the load distribution of the split star gear train, and the influence of installation error on the power split of the gear train, were studied. The effects of torque and installation error on the load coefficient of the gear train were studied using dynamic analysis software, and the efficiency of the gear train under multiple working conditions was verified and analyzed. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 418 KiB

Open AccessArticle

Finite-Time Contractively Bounded Control of Positive Linear Systems under H_∞ Performance and Its Application to Pest Management

by Liang Zhu, Baolong Zhu, Zhiguo Yan and Guolin Hu

Mathematics 2022, 10(12), 1997; https://doi.org/10.3390/math10121997 - 9 Jun 2022

Cited by 2 | Viewed by 1681

Abstract

This paper investigates the finite-time contractively bounded control issue for positive linear systems under

H_{\infty}

performance. The notion of

H_{\infty}

finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the

H_{\infty}

finite-time [...] Read more.

This paper investigates the finite-time contractively bounded control issue for positive linear systems under

H_{\infty}

performance. The notion of

H_{\infty}

finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the

H_{\infty}

finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 1991 KiB

Open AccessArticle

On The 3D VR Simulated Rubik’s Cube Game for Smart Pads

by Wen-Te Chang

Symmetry 2022, 14(6), 1193; https://doi.org/10.3390/sym14061193 - 9 Jun 2022

Cited by 2 | Viewed by 2712

Abstract

In this study, interface designs of a VR 3D-simulated Rubik’s Cube game were developed and evaluated. A 2 × 2 × 2 mixed-design ANOVA was executed, with age (younger adult/older adult), interface (arrow/intuitive), and task complexity (easy, a single symmetrical task/difficult, a bio-symmetrical [...] Read more.

In this study, interface designs of a VR 3D-simulated Rubik’s Cube game were developed and evaluated. A 2 × 2 × 2 mixed-design ANOVA was executed, with age (younger adult/older adult), interface (arrow/intuitive), and task complexity (easy, a single symmetrical task/difficult, a bio-symmetrical task) experimental design. The first three factors were between-subject designs while the latter was a within-subject design. The dependent variable was the percentage of the task performance and wayfinding questionnaire. The collected experimental data were analyzed by regression method to clarify the correlation among age, interface, task complexity, and wayfinding strategy. There were 96 subjects in the experiment, including 48 younger adults (aged from 18~22) and 48 older adults (aged from 60~85). The experimental results and statistical analysis showed that the task difficulty had a significant effect on task performance in the 3D VR Rubik’s Cube game. For the smart pad, the arrow interface was significantly more effective than the intuitive interface. The theoretical model regression analysis of the task complexity, interface, and wayfinding strategy was shown to be significant. Results showed that users may be affected either positively or negatively by the wayfinding strategy, as a higher score on familiarity indicates better VR game task performance, whereas for the usual spatial behavior wayfinding strategy, the opposite result was found for memory. These results can be used to assess VR game interface designs, taking into consideration age difference, task complexity, experiential self-report on 3D VR games, and including VR rotation navigational Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 429 KiB

Open AccessArticle

Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix

by Ninoslav Truhar and Maja Petrač

Mathematics 2022, 10(11), 1854; https://doi.org/10.3390/math10111854 - 28 May 2022

Cited by 1 | Viewed by 2235

Abstract

We present two novel results for small damped oscillations described by the vector differential equation

M \ddot{x} + C \dot{x} + K x = 0

, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. [...] Read more.

We present two novel results for small damped oscillations described by the vector differential equation

M \ddot{x} + C \dot{x} + K x = 0

, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. The first result is a novel formula for the solution X of the Lyapunov equation

A^{T} X + X A = - I

, where

A = A (v)

is obtained from

M, C (v) \in R^{n \times n}

, and

K \in R^{n \times n}

, which are the so-called mass, damping, and stiffness matrices, respectively, and

rank (M) = n - 1

. Here,

C (v)

is positive semidefinite with

rank (C (v)) = 1

. Using the obtained formula, we propose a very efficient way to compute the optimal damping matrix. The second result was obtained for a different structure, where we assume that

dim (N (M)) \geq 1

and internal damping exists (usually a small percentage of the critical damping). For this structure, we introduce a novel linearization, i.e., a novel construction of the matrix A in the Lyapunov equation

A^{T} X + X A = - I

, and a novel optimization process. The proposed optimization process computes the optimal damping

C (v)

that minimizes a function

v \mapsto trace (Z X)

(where Z is a chosen symmetric positive semidefinite matrix) using the approximation function

g (v) = c_{v} + \frac{a}{v} + b v

, for the trace function

f (v) ≐ trace (Z X (v))

. Both results are illustrated with several corresponding numerical examples. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 3265 KiB

Open AccessArticle

Linear Proportional-Integral-Differential-Robustified Continuous-Time Optimal Predictive Control for a Class of Nonlinear Systems

by Guilin Wu, Haisong Ang and Qingxi Li

Appl. Sci. 2022, 12(11), 5446; https://doi.org/10.3390/app12115446 - 27 May 2022

Cited by 2 | Viewed by 1915

Abstract

This paper presents a novel robust optimal predictive control approach for a class of nonlinear continuous-time systems perturbed by unknown disturbances. First, a new error state with a linear proportional-integral-differential (PID) structure considering current, accumulative, and derivative tracking errors is defined. Second, prediction [...] Read more.

This paper presents a novel robust optimal predictive control approach for a class of nonlinear continuous-time systems perturbed by unknown disturbances. First, a new error state with a linear proportional-integral-differential (PID) structure considering current, accumulative, and derivative tracking errors is defined. Second, prediction of the error state within the predictive periods is expressed by the error state and its high-order derivatives according to the Taylor series expansion. Last, the proposed control law as well as the main result of this paper are derived by minimizing the prediction of the error state. Numerical validation for designing a missile autopilot shows that, due to minimizing the accumulative tracking error included in the PID-structuralized new error state, the proposed approach can generate smaller steady-state tracking errors than two commonly applied continuous-time optimal predictive control approaches whether the disturbances encountered by the missile are constant or time-varying. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 4152 KiB

Open AccessArticle

Performance Evaluation of Track Curvature Sensor for Curvature Estimation in a Curved Section of Railway Tracks

by Hyun Moo Hur, Yu Jeong Shin, Jung Won Seo and Kyung Ho Moon

Appl. Sci. 2022, 12(11), 5398; https://doi.org/10.3390/app12115398 - 26 May 2022

Cited by 2 | Viewed by 2181

Abstract

Active railway vehicles such as tilting trains and active steering bogies are being developed to improve the curve running performance of railway vehicles. In this case, a technology for sensing a curve and extracting curve information such as a curvature in real time [...] Read more.

Active railway vehicles such as tilting trains and active steering bogies are being developed to improve the curve running performance of railway vehicles. In this case, a technology for sensing a curve and extracting curve information such as a curvature in real time is required. The existing railway curve detection technology has the disadvantage of requiring many calibration processes through test driving and being affected by running speed. In order to overcome these disadvantages, this paper proposes a very simple and efficient curvature estimation method. A curvature sensor prototype was manufactured and a test run was performed on the test track. As a test result compared with the track inspection data, the minimum deviation was 0.8%, the maximum deviation was 4.0% and the average deviation was 2.8%, showing good curvature measurement performance. It was also confirmed that the effect of the running speed was very small and the accuracy was high in the small curve with a large curvature. Therefore, the developed curvature measurement sensor is expected to be used very practically in the field of curvature detection and curvature extraction to control the vehicle in the curve section. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 7141 KiB

Open AccessArticle

An Efficient Numerical Model to Predict the Mechanical Response of a Railway Track in the Low-Frequency Range

by Maryam El Moueddeb, François Louf, Pierre-Alain Boucard, Franck Dadié, Gilles Saussine and Danilo Sorrentino

Vibration 2022, 5(2), 326-343; https://doi.org/10.3390/vibration5020019 - 24 May 2022

Cited by 5 | Viewed by 3026

Abstract

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical [...] Read more.

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical baselines. Historically, computation rules for traffic conditions are based on simplified analytical works, which are considerably qualitative. They have evolved through feedback and experimental campaigns to comply with the track structure evolution. An efficient methodology based on numerical simulation is needed to evaluate railway vehicle admission to answer this issue. A perspective to update these computation rules is to evaluate the structural fatigue in the rail. That is to say, fatigue is caused by bending and shear stresses. The complexity of the railway system has led to an investigation at first of the vertical response of the railway track and quantifying its contribution to the rail’s stress response. In that sense, this paper investigates the vertical track response to a moving railway vehicle at low frequencies. For this purpose, a lightweight numerical model for the track, a multi-body model for the vehicle, and a random vertical track irregularity are proposed. More explicitly, the track model consists of a two-layer discrete support model in which the rail is considered as a beam and sleepers are point masses. The rail pads and ballast layer are modelled as spring/damper couples. Numerical results show a negligible effect of track inertia forces due to high track stiffness and damping. Nevertheless, this assumption is valid for normal rail stresses but not for ballast loading, especially in the case of sleeper voids or unsupported sleepers. Hence, the prediction of the mechanical stress state in the rail for fatigue issues is achieved through a static track model where the equivalent loading is obtained from a dynamic study of a simplified vehicle model. A statistical analysis shows that the variability of the vertical track irregularity does not influence the output variabilities like the maximum in time and space of the normal and shear stress. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 416 KiB

Open AccessArticle

Optimal H₂ Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization

by Ion Necoara and Tudor-Corneliu Ionescu

Mathematics 2022, 10(10), 1765; https://doi.org/10.3390/math10101765 - 22 May 2022

Viewed by 2295

Abstract

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free [...] Read more.

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the

H_{2}

-norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal

H_{2}

-norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced

H_{2}

-error norm. We illustrate the theory on a CD-player and on a discretized heat equation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 9840 KiB

Open AccessArticle

Control Analysis of Stochastic Lagging Discrete Ecosystems

by Jinyi Zhang

Symmetry 2022, 14(5), 1039; https://doi.org/10.3390/sym14051039 - 19 May 2022

Cited by 3 | Viewed by 1387

Abstract

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial [...] Read more.

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial approximation theory, the stochastic lagged discrete ecosystems are approximately transformed as its equivalent deterministic ecosystem. Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. Finally, the effects of different random strengths on the bifurcation control and asymptotic stability control are verified by numerical simulations, which validate the correctness and effectiveness of the main results of this paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 310 KiB

Open AccessArticle

Hyperbolicity of First Order Quasi-Linear Equations

by Vladimir Vasilyev and Yuri Virchenko

Symmetry 2022, 14(5), 1024; https://doi.org/10.3390/sym14051024 - 17 May 2022

Viewed by 1612

Abstract

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of [...] Read more.

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of the matrix of the corresponding linearized first order equations system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

17 pages, 5456 KiB

Open AccessArticle

Coupling Effect Suppressed Compact Surgical Robot with 7-Axis Multi-Joint Using Wire-Driven Method

by Kicheol Yoon, Sung-Min Cho and Kwang Gi Kim

Mathematics 2022, 10(10), 1698; https://doi.org/10.3390/math10101698 - 16 May 2022

Cited by 5 | Viewed by 3399

Abstract

Currently, the most prevalent surgical treatment method is laparoscopic surgery. Robotic surgery has many advantages over laparoscopic surgery. Therefore, robotic surgery technology is currently constantly evolving. The advantages of robotic surgery are that it can minimize incision, bleeding, and sequelae. Other advantages of [...] Read more.

Currently, the most prevalent surgical treatment method is laparoscopic surgery. Robotic surgery has many advantages over laparoscopic surgery. Therefore, robotic surgery technology is currently constantly evolving. The advantages of robotic surgery are that it can minimize incision, bleeding, and sequelae. Other advantages of robotic surgery are that it can reduce hospitalization, recovery period, and side effects. The appeal of robotic surgery is that it requires fewer surgical personnel compared to laparoscopic surgery. This paper proposes an ultra-compact 7-axis vertical multi-joint robot that employs the wire-driven method for minimally invasive surgery. The proposed robot analyzes the degree of freedom and motion coupling for control. The robot joint is composed of a total of seven joints, and among them, the 7-axis joint operates the forceps. At this time, the forceps joint (#7 axis) can only operate open and close functions, while the link is bent and rotatable, regardless of position change. This phenomenon can be analyzed by Forward Kinematics. Also, when the DOF rotates, the passing wires become twisted, and the wire is generated through length change and coupling phenomenon. The maximum rotation angle of DOF is 90° and the rotating passing wire is wound by the rotation of the wire pulley. If the DOF is rotated to the full range of 120°, the second DOF will be rotated to 90°, and at this time, the coupling phenomenon caused by the first DOF rotation can be eliminated. The length change and the robot joint angle change related to the motor drive, based on the surgical robot control using the wire-driven method, are correlated, and the values for the position and direction of the end effector of the robot can be obtained through a forward kinematic analysis. The coupling problem occurring in the wire connecting the robot driving part can be solved through a kinematic analysis. Therefore, it was possible to test the position of the slave robot and the performance of the surgical forceps movement using the master system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 19922 KiB

Open AccessArticle

Long Time Simulation Analysis of Geometry Dynamics Model under Iteration

by Weiwei Sun, Long Bai, Xinsheng Ge and Lili Xia

Appl. Sci. 2022, 12(10), 4910; https://doi.org/10.3390/app12104910 - 12 May 2022

Cited by 1 | Viewed by 1663

Abstract

Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a [...] Read more.

Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a planer pendulum and a 3D pendulum were built with these three geometry expressions. According to the variation method, the dynamics models as ordinary differential equations were transformed into nonlinear equations which are solved by Newton iteration. The simulation results show that Lie group and Lie algebra calculations can conserve the geometric structure, but have different long-time behavior. The complete Lie group expression has the best long simulation behavior and has the lowest sensitivity to the time step in both planer and 3D pendulum simulations, because it saves the complete geometry of the system in the dynamics model. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 3414 KiB

Open AccessArticle

Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System

by Chenxing Cui, Fan Feng, Xiandong Meng and Xiang Liu

Mathematics 2022, 10(10), 1663; https://doi.org/10.3390/math10101663 - 12 May 2022

Cited by 5 | Viewed by 1911

Abstract

During the long-term operation of an urban railway viaduct, it is subjected to multiple cyclic loads caused by the movement of a vehicle. As a result, the fatigue life of the bridge should be fully considered during the design process. Furthermore, the bridge [...] Read more.

During the long-term operation of an urban railway viaduct, it is subjected to multiple cyclic loads caused by the movement of a vehicle. As a result, the fatigue life of the bridge should be fully considered during the design process. Furthermore, the bridge structure will be subject to environmental corrosion for an extended period of time, resulting in concrete carbonization and reinforcement corrosion, which aggravates the bridge structure’s fatigue damage. To compensate for the disadvantage of the traditional static analysis method’s inability to consider vehicle speed, a vehicle–bridge system coupled model is established, material corrosion is considered, railway bridge damage under vehicle load is analyzed, and the service life of common 30 m and 25 m span bridges is calculated. The results show that ignoring corrosion will understate the bridge damage, and vehicle speed has a significant impact on bridge fatigue life. Finally, the recommended operating speeds for 30 m span and 25 m span bridges are provided. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 4076 KiB

Open AccessArticle

Fuzzy-Based Adaptive Dynamic Surface Control for a Type of Uncertain Nonlinear System with Unknown Actuator Faults

by Xiongfeng Deng and Jiakai Wang

Mathematics 2022, 10(10), 1624; https://doi.org/10.3390/math10101624 - 10 May 2022

Cited by 5 | Viewed by 2082

Abstract

In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems and dynamic surface control technique, an adaptive [...] Read more.

In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems and dynamic surface control technique, an adaptive fuzzy control law is designed to solve the tracking control problem. In control law design, fuzzy logic systems are utilized to approximate uncertain nonlinear functions, and with the help of the dynamic surface control technique, the problem of the “explosion of complexity” can be overcome. Through stability analysis, it is confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin can be ensured by adjusting the control law parameters. Finally, the effectiveness of the proposed control law is verified by simulation examples. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

9 pages, 704 KiB

Open AccessArticle

Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding

by Xiaohui Zhang, Chengfu Ye, Shumin Zhang and Bing Yao

Mathematics 2022, 10(9), 1592; https://doi.org/10.3390/math10091592 - 7 May 2022

Cited by 4 | Viewed by 2101

Abstract

With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological [...] Read more.

With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose 6C-labeling, 6C-complementary labeling, and its reciprocal-inverse labeling, since they can be applied to build up topological coding. We show some connections between 6C-labeling and other graph labelings/colorings and show graphs admitting twin-type 6C-labelings, as well as the construction of graphs admitting twin-type 6C-labelings. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 665 KiB

Open AccessArticle

Evolutionary Dynamics of Division of Labor Games for Underwater Searching Tasks

by Minglei Xiong and Guangming Xie

Symmetry 2022, 14(5), 941; https://doi.org/10.3390/sym14050941 - 5 May 2022

Cited by 4 | Viewed by 1945

Abstract

Division of labor in self-organized groups is a problem of both theoretical significance and application value. Many application problems in the real world require efficient task allocation. We propose a model combining bio-inspiration and evolutionary game theory. This research model theoretically analyzes the [...] Read more.

Division of labor in self-organized groups is a problem of both theoretical significance and application value. Many application problems in the real world require efficient task allocation. We propose a model combining bio-inspiration and evolutionary game theory. This research model theoretically analyzes the problem of target search in unknown areas for multi-robot systems. If the robot’s operating area is underwater, the problem becomes more complicated due to its information sharing restrictions. Additionally, it drives strategy updates and calculates the fixed probability of relevant strategies, using evolutionary game theory and the commonly used Fermi function. Our study estimates the fixed probability under arbitrary selection intensity and the fixed probability and time under weak selection for the two-player game model. In the multi-player game, we get these results for weak selection, which is conducive to the coexistence of the two strategies. Moreover, the conducted simulations confirm our analysis. These results help to understand and design effective mechanisms in which self-organizing collective dynamics appears in the form of maximizing the benefits of multi-agent systems in the case of the asymmetric game. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

41 pages, 10969 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Continuous Model and Analytical Solution for Unbalance Responses

by Aiming Wang, Yujie Bi, Yun Xia, Xiaohan Cheng, Jie Yang and Guoying Meng

Appl. Sci. 2022, 12(9), 4351; https://doi.org/10.3390/app12094351 - 25 Apr 2022

Cited by 1 | Viewed by 2055

Abstract

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce [...] Read more.

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

40 pages, 4359 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Identification of Bearing Coefficients from Unbalance Responses

by Aiming Wang, Yujie Bi, Xiaohan Cheng, Jie Yang, Guoying Meng, Yun Xia and Yu Feng

Appl. Sci. 2022, 12(9), 4251; https://doi.org/10.3390/app12094251 - 22 Apr 2022

Cited by 1 | Viewed by 1631

Abstract

Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on [...] Read more.

Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on the continuous rotor dynamic analysis method. A linear functional relationship between the main complex coefficients and the cross-coupled complex coefficients is obtained, which eliminates the coupling between the coefficients and the rotor unbalance in the forward problem. Then, Algorithm I is proposed. However, it is only suitable for rolling-bearing. To solve the problem, changing the rotating speed slightly is proposed to solve the difficulty that another set of equations cannot be developed because the slope of the proposed linear function is constant when the rotating speed is maintained at a fixed speed. Then, Algorithm II, which can be applied to both rolling-bearing and oil-journal bearing, is provided. Numerical investigations are conducted to study the two methods. It is indicated that there should be a measuring point, called an adjustment point, near each bearing, whose coefficients should be identified, to obtain high identification accuracy. Moreover, the identification accuracy of the two algorithms is strongly related to sensor resolution. When the measuring errors of all the required unbalance responses are zero or the same, the identification errors are almost equal to zero. In conclusion, the proposed algorithms provide a method for monitoring the stiffness and damping coefficients of all bearings in a multi-disc and multi-span rotor under operation conditions to predict rotor dynamic behavior for the safe and steady running of rotating machines. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 5534 KiB

Open AccessArticle

Suppression of Harmonic Current in Magnetic Bearing–Rotor System with Redundant Structure

by Baixin Cheng, Xin Cheng, Shao Song, Rougang Zhou and Shuai Deng

Appl. Sci. 2022, 12(9), 4126; https://doi.org/10.3390/app12094126 - 20 Apr 2022

Viewed by 1826

Abstract

The magnetic bearing–rotor system has the advantages of no mechanical friction and active vibration control. A magnetic bearing with redundant structures provides an effective method to apply fault-tolerant control to the magnetic bearing–rotor system. In this paper, in order to improve the robustness [...] Read more.

The magnetic bearing–rotor system has the advantages of no mechanical friction and active vibration control. A magnetic bearing with redundant structures provides an effective method to apply fault-tolerant control to the magnetic bearing–rotor system. In this paper, in order to improve the robustness of a rotor suspended by a magnetic bearing with redundant structures, the harmonic current suppression approach is proposed. Firstly, the generation mechanism of harmonic current in the magnetic bearing–rotor system is analyzed. Secondly, on the basis of the current distribution theory of magnetic bearing with redundant structures, the linearization model of electromagnetic force is established. Then, the eight-pole symmetrical radial magnetic bearing is taken as the research object, and the control system model with a multi-excitation disturbance source is established under the condition of no coil failure. Lastly, considering the periodicity of disturbance signals, a repetitive controller that is suitable for magnetic bearing with redundant structures is proposed in this paper, Moreover, in order to verify the effectiveness of the proposed control strategy, we inserted the repetitive controller into the original controller applied to the magnetically levitated rotor with redundant structures, and the corresponding simulation was carried out. The results demonstrate that the repetitive control method proposed in this paper can effectively suppress the harmonic current and improve the suspension accuracy of the rotor supported by the magnetic bearing with redundant structures. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 6004 KiB

Open AccessArticle

Third-Order Superharmonic Resonance Analysis and Control in a Nonlinear Dynamical System

by Ali Kandil, Yasser S. Hamed, Mohamed S. Mohamed, Jan Awrejcewicz and Maksymilian Bednarek

Mathematics 2022, 10(8), 1282; https://doi.org/10.3390/math10081282 - 12 Apr 2022

Cited by 7 | Viewed by 2550

Abstract

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for [...] Read more.

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for stability using Floquet exponents. The cubic-position control gain is adjusted in order to suppress the model’s steady oscillations. In addition, the negative-velocity control gain is adjusted in order to shrink the period of the transient oscillations. Several plots are included to relate the car’s oscillatory amplitude with the model’s different parameters pre- and post-control so that we can determine the optimum conditions for running the model safely. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

42 pages, 8448 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotors: A Theoretical and Numerical Investigation of the Identification of Rotor Unbalance from Unbalance Responses

by Aiming Wang, Yujie Bi, Yu Feng, Jie Yang, Xiaohan Cheng and Guoying Meng

Appl. Sci. 2022, 12(8), 3865; https://doi.org/10.3390/app12083865 - 11 Apr 2022

Cited by 4 | Viewed by 2074

Abstract

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from [...] Read more.

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 318 KiB

Open AccessArticle

Controllability and Hyers–Ulam Stability of Differential Systems with Pure Delay

by Ahmed M. Elshenhab and Xingtao Wang

Mathematics 2022, 10(8), 1248; https://doi.org/10.3390/math10081248 - 11 Apr 2022

Cited by 13 | Viewed by 1923

Abstract

Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions is used to obtain the controllability and Hyers–Ulam [...] Read more.

Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions is used to obtain the controllability and Hyers–Ulam stability results. By introducing a delay Gramian matrix, we establish some sufficient and necessary conditions for the controllability of linear delay differential systems. In addition, by applying Krasnoselskii’s fixed point theorem, we establish some sufficient conditions of controllability and Hyers–Ulam stability of nonlinear delay differential systems. Our results improve, extend, and complement some existing ones. Finally, two examples are given to illustrate the main results. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

19 pages, 3374 KiB

Open AccessArticle

Numerical Assessment of Dipole Interaction with the Single-Phase Nanofluid Flow in an Enclosure: A Pseudo-Transient Approach

by Rashid Ayub, Shabbir Ahmad, Sohail Ahmad, Yasmeen Akhtar, Mohammad Mahtab Alam and Omar Mahmoud

Materials 2022, 15(8), 2761; https://doi.org/10.3390/ma15082761 - 9 Apr 2022

Cited by 25 | Viewed by 2063

Abstract

Nanofluids substantially enhance the physical and thermal characteristics of the base or conducting fluids specifically when interacting with the magnetic field. Several engineering processes like geothermal energy extraction, metal casting, nuclear reactor coolers, nuclear fusion, magnetohydrodynamics flow meters, petrochemicals, and pumps incorporate magnetic [...] Read more.

Nanofluids substantially enhance the physical and thermal characteristics of the base or conducting fluids specifically when interacting with the magnetic field. Several engineering processes like geothermal energy extraction, metal casting, nuclear reactor coolers, nuclear fusion, magnetohydrodynamics flow meters, petrochemicals, and pumps incorporate magnetic field interaction with the nanofluids. On the other hand, an enhancement in heat transfer due to nanofluids is essentially required in various thermal systems. The goal of this study is to figure out that how much a magnetic field affects nanofluid flow in an enclosure because of a dipole. The nanofluid is characterized using a single-phase model, and the governing partial differential equations are computed numerically. A Pseudo time based numerical algorithm is developed to numerically solve the problem. It can be deduced that the Reynolds number and the magnetic parameter have a low effect on the Nusselt number and skin friction. The Nusselt number rises near the dipole location because of an increase in the magnetic parameter

M n

and the Reynolds number

Re

. The imposed magnetic field alters the region of high temperature nearby the dipole, while newly generated vortices rotate in alternate directions. Furthermore, nanoparticle volume fraction causes a slight change in the skin friction while it marginally reduces the Nusselt number. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 5779 KiB

Open AccessArticle

Adaptive, Observer-Based Synchronization of Different Chaotic Systems

by Jacek Kabziński and Przemysław Mosiołek

Appl. Sci. 2022, 12(7), 3394; https://doi.org/10.3390/app12073394 - 27 Mar 2022

Cited by 10 | Viewed by 2054

Abstract

In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is [...] Read more.

In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 5507 KiB

Open AccessArticle

Robust Nonlinear Non-Referenced Inertial Frame Multi-Stage PID Controller for Symmetrical Structured UAV

by Faruk Takaoğlu, Ali Alshahrani, Naim Ajlouni, Firas Ajlouni, Basil Al Kasasbah and Adem Özyavaş

Symmetry 2022, 14(4), 689; https://doi.org/10.3390/sym14040689 - 26 Mar 2022

Cited by 3 | Viewed by 2523

Abstract

The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the [...] Read more.

The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer’s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller’s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for “new solutions” by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 6927 KiB

Open AccessArticle

1/3 Order Subharmonic Resonance Control of a Mass-Damper-Spring Model via Cubic-Position Negative-Velocity Feedback

by Ali Kandil, Yasser S. Hamed, Khadijah M. Abualnaja, Jan Awrejcewicz and Maksymilian Bednarek

Symmetry 2022, 14(4), 685; https://doi.org/10.3390/sym14040685 - 25 Mar 2022

Cited by 8 | Viewed by 2407

Abstract

A cubic-position negative-velocity (CPNV) feedback controller is proposed in this research in order to suppress the nontrivial oscillations of the

1 / 3

order subharmonic resonance of a mass-damper-spring model. Based on the Krylov–Bogoliubov (KB) averaging method, the model’s equation of motion is [...] Read more.

A cubic-position negative-velocity (CPNV) feedback controller is proposed in this research in order to suppress the nontrivial oscillations of the

1 / 3

order subharmonic resonance of a mass-damper-spring model. Based on the Krylov–Bogoliubov (KB) averaging method, the model’s equation of motion is approximately solved and tested for stability. The nontrivial solutions region is plotted to determine where these solutions occur and try to quench them. The controller parameters can play crucial roles in eliminating such regions, keeping only the trivial solutions, and improving the transient response of the car’s oscillations. Different response curves and relations are included in this study to provide the reader a wide overview of the control process. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

9 pages, 232 KiB

Open AccessArticle

Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria

by Ziad Zahreddine

Symmetry 2022, 14(3), 603; https://doi.org/10.3390/sym14030603 - 18 Mar 2022

Cited by 5 | Viewed by 3554

Abstract

It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such [...] Read more.

It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such observations lead to the search for a unified approach to the study of root distribution for real and complex polynomials, with respect to the left-half plane for continuous-time systems (Routh–Hurwitz stability) and with respect to the unit disc for discrete-time systems (Schur–Cohn stability). This paper is a further contribution toward this objective. We present, in a systematic way, the similarities, and yet, the differences between these two types of stability, and we highlight the symmetry that exists between them. We also illustrate how results on the stability of continuous-time systems are conveyed to the stability of discrete-time systems through the proposed techniques. It should be mentioned that the results on Schur–Cohn stability are known to be harder to obtain than Routh–Hurwitz stability ones, giving more credibility to the proposed approach. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

26 pages, 5568 KiB

Open AccessArticle

Runtime Software Architecture-Based Reliability Prediction for Self-Adaptive Systems

by Qiuying Li, Minyan Lu, Tingyang Gu and Yumei Wu

Symmetry 2022, 14(3), 589; https://doi.org/10.3390/sym14030589 - 16 Mar 2022

Viewed by 2950

Abstract

Modern software systems need to autonomously adapt their behavior at runtime in order to maintain their utility in response to continuous environmental changes. Most studies on models at runtime focus on providing suitable techniques to manage the complexity of software at runtime but [...] Read more.

Modern software systems need to autonomously adapt their behavior at runtime in order to maintain their utility in response to continuous environmental changes. Most studies on models at runtime focus on providing suitable techniques to manage the complexity of software at runtime but neglect reliability caused by adaptation activities. Therefore, adaptive behaviors may lead to a decrease in reliability, which may result in severe financial loss or life damage. Runtime software architecture (RSA) is an abstract of a running system, which describes the elements of the current system, the states of these elements and the relation between the elements and their states at runtime. The main difference between RSA and software architecture at design time (DSA) is that RSA has a causal connection with the running system, whereas DSA does not. However, RSA and DSA have both symmetry and asymmetry in software architecture. To ensure that architecture-centric software can provide reliable services after adaptation adjustment, a method is proposed to analyze the impact of changes caused by adaptation strategy on the overall software reliability, which will be predicted at the runtime architecture model layer. Based on a Java platform, through non-intrusive monitoring, an RSA behavioral model is obtained followed by runtime reliability analysis model. Following this, reliability prediction results are obtained through a discrete-time Markov chain (DTMC). Finally, an experiment is conducted to verify the feasibility of the proposed method. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 865 KiB

Open AccessArticle

Event-Triggered Cooperative Predictive Control for Networked Multi-Agent Systems with Random Delays and Packet Dropouts

by Zhonghua Pang, Tao Du, Changbing Zheng and Chao Li

Symmetry 2022, 14(3), 541; https://doi.org/10.3390/sym14030541 - 7 Mar 2022

Cited by 3 | Viewed by 2424

Abstract

This paper addresses the cooperative output tracking control problem for a class of leader-following linear heterogeneous networked multi-agent systems subject to random network delays and packet dropouts in the feedback and forward channels of each agent. A state observer is established at the [...] Read more.

This paper addresses the cooperative output tracking control problem for a class of leader-following linear heterogeneous networked multi-agent systems subject to random network delays and packet dropouts in the feedback and forward channels of each agent. A state observer is established at the plant side of each agent, and an event-triggering transmission mechanism is introduced to decide which state estimate is transmitted to the corresponding controller so as to save the network resources of the feedback channel. To further compensate for the negative effects of those random communication constraints and the event trigger, a cooperative predictive control scheme with proportional and integral actions is proposed. Then, a necessary and sufficient condition is derived for the stability of the resulting closed-loop system. Finally, simulation results are given to show the effectiveness of the proposed scheme. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 384 KiB

Open AccessArticle

Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities

by Zhen Yang and Zhengqiu Zhang

Mathematics 2022, 10(5), 835; https://doi.org/10.3390/math10050835 - 6 Mar 2022

Cited by 14 | Viewed by 2395

Abstract

In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for [...] Read more.

In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

32 pages, 486 KiB

Open AccessArticle

Infinite–Dimensional Bifurcations in Spatially Distributed Delay Logistic Equation

by Sergey Kashchenko

Mathematics 2022, 10(5), 775; https://doi.org/10.3390/math10050775 - 28 Feb 2022

Cited by 3 | Viewed by 1953

Abstract

This paper investigates the questions about the local dynamics in the neighborhood of the equilibrium state for the spatially distributed delay logistic equation with diffusion. The critical cases in the stability problem are singled out. The equations for their invariant manifolds that determine [...] Read more.

This paper investigates the questions about the local dynamics in the neighborhood of the equilibrium state for the spatially distributed delay logistic equation with diffusion. The critical cases in the stability problem are singled out. The equations for their invariant manifolds that determine the structure of the solutions in the equilibrium state neighborhood are constructed. The dominant bulk of this paper is devoted to the consideration of the most interesting and important cases of either the translation (advection) coefficient is large enough or the diffusion coefficient is small enough. Both of this cases convert the original problem to a singularly perturbed one. It is shown that under these conditions the critical cases are infinite–dimensional in the problems of the equilibrium state stability for the singularly perturbed problems. This means that infinitely many roots of the characteristic equations of the corresponding linearized boundary value problems tend to the imaginary axis as the small parameter tends to zero. Thus, we are talking about infinite–dimensional bifurcations. Standard approaches to the study of the local dynamics based on the application of the invariant integral manifolds methods and normal forms methods are not applicable. Therefore, special methods of infinite–dimensional normalization have been developed which allow one to construct special nonlinear boundary value problems called quasinormal forms. Their nonlocal dynamics determine the behavior of the initial boundary value problem solutions in the neighborhood of the equilibrium state. The bifurcation features arising in the case of different boundary conditions are illustrated. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 1229 KiB

Open AccessArticle

Adaptive Sliding Mode Attitude Control of Quadrotor UAVs Based on the Delta Operator Framework

by Bochao Zheng, Yuewen Wu, Hui Li and Zhipeng Chen

Symmetry 2022, 14(3), 498; https://doi.org/10.3390/sym14030498 - 28 Feb 2022

Cited by 12 | Viewed by 3201

Abstract

In this paper, a novel adaptive sliding-mode control algorithm is proposed for the attitude control of quadrotor unmanned aerial vehicles (UAVs) under the delta operator framework. First, the delta operator technique is used to discretize the attitude control systems of a quadrotor UAV. [...] Read more.

In this paper, a novel adaptive sliding-mode control algorithm is proposed for the attitude control of quadrotor unmanned aerial vehicles (UAVs) under the delta operator framework. First, the delta operator technique is used to discretize the attitude control systems of a quadrotor UAV. Then, based on the linear matrix inequality technique, a linear sliding surface is designed to ensure the asymptotical stability of the quadrotor UAV attitude control system during the sliding motion process. Second, by the estimated external disturbance using a radical basis function (RBF) neural network, an adaptive sliding-mode attitude controller is designed such that the states of the quadrotor UAV attitude systems can be driven towards the desired sliding surface, and thus the attitude control objective of the qudarotor UAV is achieved. Compared with the traditional adaptive sliding-mode control algorithm, the proposed adaptive sliding-mode control algorithm can effectively realize the attitude control of a quadrotor UAV subject to strong disturbances and couplings. Finally, comparisons of the simulation results verify the effectiveness and superiority of the control algorithm proposed in this paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

30 pages, 16830 KiB

Open AccessArticle

Hydrocode Investigations of Terminal Astroballistics Problems during the Hypothetical Future Planetary Defense System’s Space Mission

by Maciej Mroczkowski, Stanisław Kachel and Adam Kozakiewicz

Materials 2022, 15(5), 1752; https://doi.org/10.3390/ma15051752 - 25 Feb 2022

Viewed by 2981

Abstract

The article is devoted to the preliminary concept of the Future Planetary Defense System (FPDS) emphasizing astroballistics. This paper is intended to support international efforts to improve the planetary security of Earth. The work covers three areas of knowledge: astronautics, astrodynamics, and astroballistics. [...] Read more.

The article is devoted to the preliminary concept of the Future Planetary Defense System (FPDS) emphasizing astroballistics. This paper is intended to support international efforts to improve the planetary security of Earth. The work covers three areas of knowledge: astronautics, astrodynamics, and astroballistics. The most important part of the presented article is dynamic, contact combat modeling against small, deformable celestial bodies. For these purposes, the original, proprietary hydrocode of the free particle method (HEFPM-G) with gravity was used. The main aim of combat is to redirect potentially hazardous objects (PHOs) to orbits safe for Earth or destroy them. This concept’s first task is to find, prepare, and use dynamic three-dimensional models of the motion of celestial bodies and spacecraft or human-crewed spaceships in the solar system’s relativistic frame. The second task is to prepare the FPDS’ architecture and computer simulation space missions’ initial concepts in the internal part of the solar system. The third and main task covers simulating, using hydrocodes, and selected methods of fighting 100 m diameter rock material asteroids. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

26 pages, 647 KiB

Open AccessArticle

A Quasi-3D Refined Theory for the Vibration of Functionally Graded Plates Resting on Visco-Winkler-Pasternak Foundations

by Mashhour A. Alazwari and Ashraf M. Zenkour

Mathematics 2022, 10(5), 716; https://doi.org/10.3390/math10050716 - 24 Feb 2022

Cited by 11 | Viewed by 2211

Abstract

This article establishes the vibrational behavior of functionally graded plates embedded in a viscoelastic medium. The quasi-3D elasticity equations are used for this purpose. The three-parameter Visco-Winkler-Pasternak model is employed to give the interaction between the viscoelastic foundation and the presented plate. Hamilton’s [...] Read more.

This article establishes the vibrational behavior of functionally graded plates embedded in a viscoelastic medium. The quasi-3D elasticity equations are used for this purpose. The three-parameter Visco-Winkler-Pasternak model is employed to give the interaction between the viscoelastic foundation and the presented plate. Hamilton’s principle is applied to derive the governing dynamic equations. Many validation examples are presented. Additional benchmark results are tabulated for future comparisons. The effects of various parameters like geometrical, material properties, and viscoelastic foundations on the vibrational frequencies of homogeneous and functionally graded plates are investigated. The frequencies increase as all parameters increase except the functionally graded power-law index for which its increase causes a decrease in the frequency value. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 661 KiB

Open AccessArticle

(α^{F}, α^{\bar{F}})

-Information Fusion Generated by Information Segmentation and Its Intelligent Retrieval

by Xiuquan Zhang, Lin Shen and Kaiquan Shi

Mathematics 2022, 10(5), 713; https://doi.org/10.3390/math10050713 - 24 Feb 2022

Cited by 2 | Viewed by 1723

Abstract

Making use of the mathematical model with dynamic features and attribute disjunctive characteristics, the new concepts of

α^{F}

-information segmentation,

α^{\bar{F}}

-information segmentation,

(α^{F}, α^{\bar{F}})

-information segmentation and their attribute characteristics are given, and [...] Read more.

Making use of the mathematical model with dynamic features and attribute disjunctive characteristics, the new concepts of

α^{F}

-information segmentation,

α^{\bar{F}}

-information segmentation,

(α^{F}, α^{\bar{F}})

-information segmentation and their attribute characteristics are given, and the intelligent acquisition of matrix reasoning and information segmentation is given, as well as the information segmentation theorem. Moreover, the equivalence between information segmentation and information fusion is discussed, and the information fusion intelligent acquisition intelligent retrieval algorithm is given. Based on these theoretical results, the intelligent information fusion retrieval algorithm and its simple application in health big data are presented. In conclusion, the results presented in this paper are entirely based on new ideas. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

25 pages, 9682 KiB

Open AccessArticle

Dynamic Analysis of Quasi-Zero Stiffness Pneumatic Vibration Isolator

by Ngoc Yen Phuong Vo and Thanh Danh Le

Appl. Sci. 2022, 12(5), 2378; https://doi.org/10.3390/app12052378 - 24 Feb 2022

Cited by 8 | Viewed by 2734

Abstract

This paper focuses on analyzing the dynamic response of an innovated quasi-zero stiffness pneumatic vibration isolator (QZSPVI) using two mechanisms, including wedge and semicircle cam. Different from other studies relating quasi-zero stiffness isolation system, the pneumatic cylinder in this paper works as an [...] Read more.

This paper focuses on analyzing the dynamic response of an innovated quasi-zero stiffness pneumatic vibration isolator (QZSPVI) using two mechanisms, including wedge and semicircle cam. Different from other studies relating quasi-zero stiffness isolation system, the pneumatic cylinder in this paper works as an air spring in order to easily adjust the dynamic stiffness of the proposed system according to the change of the isolated load through regulating the pressure. Firstly, the dynamic stiffness of the QZSPVI will be analyzed. Then, the condition for which the minimum dynamic stiffness is quasi-zero around the equilibrium position is also determined. The fundamental resonance response of the QZSPVI subjected to the externally harmonic force is analyzed through multi-scale method and the numerical simulations are verified. Secondly, due to exiting relative sliding frictional phenomenon between the cylinder and piston, instead of an experiment, another key content of this work is to identify the friction force model of the cylinder through virtual prototyping model. From this identified result, the complex dynamic response of the QZSPVI and coexistence of multiple solutions will be discovered by realizing the direct integration of the original dynamic equation through using the 5th-order Runge–Kutta algorithm. The analysis and simulation results clearly show the advantages of the proposed model against the equivalent pneumatic vibration isolator (EPVI), which only employs the wedge mechanism. This research will offer a useful insight into design and QZSPVI in practice. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 557 KiB

Open AccessArticle

Lower Triangular Factor-Based Fault Estimation and Fault-Tolerant Control for Descriptor Markovian Jump Systems with Multiple Faults

by Xiaoming Su, Haoda Shi and Adiya Bao

Symmetry 2022, 14(2), 382; https://doi.org/10.3390/sym14020382 - 15 Feb 2022

Viewed by 2242

Abstract

This paper considers the observer-based fault estimation and fault-tolerant control for descriptor Markovian jump systems (DMJSs). The goal of this paper is to estimate the actuator faults, sensor faults, and the state simultaneously, and then design a controller based on the estimation to [...] Read more.

This paper considers the observer-based fault estimation and fault-tolerant control for descriptor Markovian jump systems (DMJSs). The goal of this paper is to estimate the actuator faults, sensor faults, and the state simultaneously, and then design a controller based on the estimation to stabilize the DMJS. Firstly, the state, actuator faults, and sensor faults are extended to new state variables to obtain an augmented system. Then, a lower triangular factor-based estimation observer (LTFEO) is proposed to estimate the state and multiple faults and to eliminate the influence of sensor faults. It is proved that the descriptor error system is derivative input-to-state stable (DISS) with respect to the derivative of the faults. Furthermore, based on the fault estimation, a fault-tolerant control scheme is proposed to guarantee the overall closed-loop system DISS. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme and control strategy. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 5650 KiB

Open AccessArticle

Effect of Global and Local Refutation Mechanism on Rumor Propagation in Heterogeneous Network

by Liang’an Huo and Yuqing Zhang

Mathematics 2022, 10(4), 586; https://doi.org/10.3390/math10040586 - 14 Feb 2022

Cited by 10 | Viewed by 1969

Abstract

In the process of rumors propagation, the behavior of individuals to propagation or refutation is not only influenced by the surrounding global environment but also the local environment. In this paper, a modified rumor propagation model is proposed considering the global and local [...] Read more.

In the process of rumors propagation, the behavior of individuals to propagation or refutation is not only influenced by the surrounding global environment but also the local environment. In this paper, a modified rumor propagation model is proposed considering the global and local effects of the rumor refutation mechanism and the activity rate of individuals in a heterogeneous network, and the dynamics process of the rumor propagation is derived by using the mean-field equation. Combining theoretical proving and simulation analysis, it shows that the critical threshold of rumor propagation has a great relationship with individual activity rates and global and local effects of the rumor refutation mechanism. The greater the government’s efforts to refute rumors, the lower the critical threshold of rumor propagation and the smaller the final rumor size. While relatively, people are much more likely to believe the global rumor refutation information taken with official information, local rumor refutation information has little influence on rumor propagation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 3136 KiB

Open AccessArticle

Free Vibration of FG-CNTRCs Nano-Plates/Shells with Temperature-Dependent Properties

by Ammar Melaibari, Ahmed Amine Daikh, Muhammad Basha, Ahmed W. Abdalla, Ramzi Othman, Khalid H. Almitani, Mostafa A. Hamed, Alaa Abdelrahman and Mohamed A. Eltaher

Mathematics 2022, 10(4), 583; https://doi.org/10.3390/math10040583 - 13 Feb 2022

Cited by 57 | Viewed by 2939

Abstract

This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in [...] Read more.

This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geometries, such as plate (infinite radii), spherical, cylindrical, hyperbolic-paraboloid and elliptical-paraboloid are considered in the analysis. By employing Hamilton’s variational principle, the equations of motion are derived based on hyperbolic sine function shear deformation theory. Then, the derived equations are solved analytically using the Galerkin approach. Two types of material distribution are proposed. Higher-order nonlocal strain gradient theory is employed to capture influences of shear deformation, length scale parameter (nonlocal) and material/microstructurescale parameter (gradient). Temperature-dependent material properties are considered. The validation of the proposed mathematical model is presented. Detailed parametric analyses are carried out to highlight the effects of the carbon nanotubes (CNT) distribution pattern, the thickness stretching, the geometry of the plate/shell, the boundary conditions, the total number of layers, the length scale and the material scale parameters, on the vibrational frequencies of CNTRC laminated nanoplates and nanoshells. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

26 pages, 3344 KiB

Open AccessArticle

The Gaussian Mutational Barebone Dragonfly Algorithm: From Design to Analysis

by Li Yuan, Fangjun Kuang, Siyang Zhang and Huiling Chen

Symmetry 2022, 14(2), 331; https://doi.org/10.3390/sym14020331 - 6 Feb 2022

Cited by 5 | Viewed by 2931

Abstract

The dragonfly algorithm is a swarm intelligence optimization algorithm based on simulating the swarming behavior of dragonfly individuals. An efficient algorithm must have a symmetry of information between the participating entities. An improved dragonfly algorithm is proposed in this paper to further improve [...] Read more.

The dragonfly algorithm is a swarm intelligence optimization algorithm based on simulating the swarming behavior of dragonfly individuals. An efficient algorithm must have a symmetry of information between the participating entities. An improved dragonfly algorithm is proposed in this paper to further improve the global searching ability and the convergence speed of DA. The improved DA is named GGBDA, which adds Gaussian mutation and Gaussian barebone on the basis of DA. Gaussian mutation can randomly update the individual positions to avoid the algorithm falling into a local optimal solution. Gaussian barebone can quicken the convergent speed and strengthen local exploitation capacities. Enhancing algorithm efficiency relative to the symmetric concept is a critical challenge in the field of engineering design. To verify the superiorities of GGBDA, this paper sets 30 benchmark functions, which are taken from CEC2014 and 4 engineering design problems to compare GGBDA with other algorithms. The experimental result show that the Gaussian mutation and Gaussian barebone can effectively improve the performance of DA. The proposed GGBDA, similar to the DA, presents improvements in global optimization competence, search accuracy, and convergence performance. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 726 KiB

Open AccessArticle

Global Dynamics of a Vibro-Impact Energy Harvester

by Zhenbang Cao, Haotong Ma, Xuegang Yu, Jianliang Shi, Hu Yang, Yi Tan and Ge Ren

Mathematics 2022, 10(3), 472; https://doi.org/10.3390/math10030472 - 1 Feb 2022

Cited by 1 | Viewed by 1869

Abstract

In this paper, we consider a two-sided vibro-impact energy harvester described as a forced cylindrical capsule inclined at a horizontal angle, and the motion of the ball inside the capsule follows from the impacts with the capsule ends and gravity. Two distinct cases [...] Read more.

In this paper, we consider a two-sided vibro-impact energy harvester described as a forced cylindrical capsule inclined at a horizontal angle, and the motion of the ball inside the capsule follows from the impacts with the capsule ends and gravity. Two distinct cases of dynamical behavior are investigated: the nondissipative and dissipative cases, where the dissipation is given by a restitution coefficient of impacts. We show that the dynamics of the system are described by the use of a 2D implicit map written in terms of the variables’ energy and time when the ball leaves the moving capsule ends. More precisely, in the nondissipative case, we analytically show that this map is area-preserving and the existence of invariant curves for some rotation number with Markoff constant type is proved according to Moser’s twist theorem in high energy. The existence of invariant curves implies that the kinetic energy of the ball is always bounded, and hence, the structure of system is not destroyed by the impacts of the ball. Furthermore, by numerical analysis we also show that the dynamical behavior of this system is regular, mainly containing periodic points, invariant curves and Aubry–Mather sets. After introducing dissipation, the dissipation destroys the regular dynamical behavior of the nondissipative case, and a periodic point with low energy is generated. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 1544 KiB

Open AccessArticle

Adaptive Dual Synchronization of Fractional-Order Chaotic System with Uncertain Parameters

by Dehui Liu, Tianzeng Li and Yu Wang

Mathematics 2022, 10(3), 470; https://doi.org/10.3390/math10030470 - 31 Jan 2022

Cited by 10 | Viewed by 2181

Abstract

The problem of the dual synchronization of two different fractional-order chaotic systems with uncertain parameters is studied. This paper introduces a synchronization method in accordance with Lyapunov stability theory, and the adaptive controllers and adaptive laws are designed to realize the dual synchronization [...] Read more.

The problem of the dual synchronization of two different fractional-order chaotic systems with uncertain parameters is studied. This paper introduces a synchronization method in accordance with Lyapunov stability theory, and the adaptive controllers and adaptive laws are designed to realize the dual synchronization of fractional order chaotic systems. Finally, two numerical examples of unknown different fractional-order chaotic systems are also given to prove the accuracy of the theory in the paper, and the effectiveness and performance of the proposed adaptive dual synchronization strategy are verified by simulation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 5767 KiB

Open AccessArticle

Prediction of Concrete Fragments Amount and Travel Distance under Impact Loading Using Deep Neural Network and Gradient Boosting Method

by Kyeongjin Kim, WooSeok Kim, Junwon Seo, Yoseok Jeong, Meeju Lee and Jaeha Lee

Materials 2022, 15(3), 1045; https://doi.org/10.3390/ma15031045 - 28 Jan 2022

Cited by 8 | Viewed by 2560

Abstract

In the present study, the amount of fragments generated and their travel distances due to vehicle collision with concrete median barrier (CMB) was analyzed and predicted. In this regard, machine learning was applied to the results of numerical analysis, which were developed by [...] Read more.

In the present study, the amount of fragments generated and their travel distances due to vehicle collision with concrete median barrier (CMB) was analyzed and predicted. In this regard, machine learning was applied to the results of numerical analysis, which were developed by comparing with field test. The numerical model was developed using smoothed particle hydrodynamics (SPH). SPH is a mesh-free method that can be used to predict the amount of fragments and their travel distances from concrete structures under impact loading. In addition, deep neural network (DNN) and gradient boosting machine (GBM) were also employed as machine learning methods. In this study, the results of DNN, GBM, and numerical analysis were then compared with the conducted field test. Such comparisons revealed that numerical analysis generated lower error than both DNN and GBM. When prediction results of both the amount of fragments and their travel distances were considered, the result of DNN showed smaller errors than that of GBM. Therefore, in studies where machine learning is used to predict the amount of fragments and their travel distances, careful selection of an appropriate method from the various available machine learning methods such as DNN, GBM, and random forest is absolutely important. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 2145 KiB

Open AccessArticle

Stochastic Analysis of Nonlinear Cancer Disease Model through Virotherapy and Computational Methods

by Ali Raza, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed and Muhammad Mohsin

Mathematics 2022, 10(3), 368; https://doi.org/10.3390/math10030368 - 25 Jan 2022

Cited by 23 | Viewed by 3207

Abstract

Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer [...] Read more.

Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer cells, viral therapy, and immune response. In this model, the cell population has four parts, namely uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). This study presents the analysis of the stochastic cancer virotherapy model in the cell population dynamics. The model results have restored the properties of the biological problem, such as dynamical consistency, positivity, and boundedness, which are the considerable requirements of the models in these fields. The existing computational methods, such as the Euler Maruyama, Stochastic Euler, and Stochastic Runge Kutta, fail to restore the abovementioned properties. The proposed stochastic nonstandard finite difference method is efficient, cost-effective, and accommodates all the desired feasible properties. The existing standard stochastic methods converge conditionally or diverge in the long run. The solution by the nonstandard finite difference method is stable and convergent over all time steps. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

26 pages, 6419 KiB

Open AccessArticle

Performance Analysis of a Waste-to-Energy System Integrated with the Steam–Water Cycle and Urea Hydrolysis Process of a Coal-Fired Power Unit

by Yuanyuan Zhang, Lai Wei, Xin Gao, Heng Chen, Qiubai Li, Kai Zhang and Qilong Huang

Appl. Sci. 2022, 12(2), 866; https://doi.org/10.3390/app12020866 - 15 Jan 2022

Cited by 2 | Viewed by 2831

Abstract

An innovative hybrid energy system consisting of a waste-to-energy unit and a coal-fired power unit is designed to enhance the energy recovery of waste and decrease the investment costs of waste-to-energy unit. In this integrated design, partial cold reheat steam of the coal-fired [...] Read more.

An innovative hybrid energy system consisting of a waste-to-energy unit and a coal-fired power unit is designed to enhance the energy recovery of waste and decrease the investment costs of waste-to-energy unit. In this integrated design, partial cold reheat steam of the coal-fired unit is heated by the waste-to-energy boiler’s superheater. The heat required for partial preheated air of waste-to-energy unit and its feedwater are supplied by the feedwater of CFPU. In addition, an additional evaporator is deployed in the waste-to-energy boiler, of which the outlet stream is utilized to provide the heat source for the urea hydrolysis unit of coal-fired power plant. The stand-alone and proposed designs are analyzed and compared through thermodynamic and economic methods. Results indicate that the net total energy efficiency increases from 41.84% to 42.12%, and the net total exergy efficiency rises from 41.19% to 41.46% after system integration. Moreover, the energy efficiency and exergy efficiency of waste-to-energy system are enhanced by 10.48% and 9.92%, respectively. The dynamic payback period of new waste-to-energy system is cut down from 11.39 years to 5.48 years, and an additional net present value of $14.42 million is got than before. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 2391 KiB

Open AccessArticle

Sensitivity Analysis of Holdback Bar Release Load during Catapult-Assisted Takeoff of Carrier-Based Aircraft

by Enze Zhu, Zhipeng Zhang and Hong Nie

Appl. Sci. 2022, 12(2), 785; https://doi.org/10.3390/app12020785 - 13 Jan 2022

Viewed by 2464

Abstract

The release load of holdback bar will affect the safety of catapult-assisted takeoff of carrier-based aircraft, and the accurate control of releasing the load will ensure success. The magnitude and the control accuracy of release load are important parameters which impact the takeoff [...] Read more.

The release load of holdback bar will affect the safety of catapult-assisted takeoff of carrier-based aircraft, and the accurate control of releasing the load will ensure success. The magnitude and the control accuracy of release load are important parameters which impact the takeoff performance, therefore unstable release load and insufficient release precision are the main factors affecting the takeoff safety. In this paper, mechanical models of the carrier-based aircraft in the catapult-assisted takeoff tensioning state and gliding state after release are established based on multi-body dynamics, contact mechanics and tribological theory, and the influence of the release load of the holdback bar on the catapult-assisted takeoff performance is analyzed. Furthermore, a kinetic model of the holdback bar device is established, and the kinetic characteristics of the release process of the holdback bar are studied. Based on the kinetic model and friction model of the holdback bar, the influencing factors of the sensitivity of the holdback bar release load are analyzed and the structural parameters are optimized. The results show that the released load decreases slowly with the increase of the contact surface angle of the holdback bar structure and increases rapidly when that angle reaches the critical value; besides, the release load increases slowly with the increase of the friction coefficient of the contact surface and increases faster when the critical friction coefficient is reached. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 21978 KiB

Open AccessArticle

Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System

by Biao Liu and Ranchao Wu

Mathematics 2022, 10(2), 243; https://doi.org/10.3390/math10020243 - 13 Jan 2022

Cited by 5 | Viewed by 2437

Abstract

The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper. The linear stability of the fixed points to [...] Read more.

The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper. The linear stability of the fixed points to such spatiotemporal discrete system is analyzed by stability theory. By using the bifurcation theory, the center manifold theory and the Turing instability theory, the Turing instability conditions in flip bifurcation and Neimark–Sacker bifurcation are considered, respectively. To illustrate the above theoretical results, numerical simulations are carried out, such as bifurcation diagram, maximum Lyapunov exponents, phase orbits, and pattern formations. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 521 KiB

Open AccessArticle

A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

by Ashraf M. Zenkour, Mashhour A. Alazwari and Ahmed F. Radwan

Mathematics 2022, 10(2), 234; https://doi.org/10.3390/math10020234 - 13 Jan 2022

Cited by 3 | Viewed by 1914

Abstract

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered [...] Read more.

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 9219 KiB

Open AccessArticle

Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

by Gerardo Ayala-Jaimes, Gilberto Gonzalez-Avalos, Noe Barrera Gallegos, Aaron Padilla Garcia and Juancarlos Méndez-Barriga

Symmetry 2022, 14(1), 104; https://doi.org/10.3390/sym14010104 - 8 Jan 2022

Viewed by 1842

Abstract

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with [...] Read more.

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 9009 KiB

Open AccessArticle

Dynamic Response and Failure Process of a Counter-Bedding Rock Slope under Strong Earthquake Conditions

by Ming-Zhu Guo, Kun-Sheng Gu and Chen Wang

Symmetry 2022, 14(1), 103; https://doi.org/10.3390/sym14010103 - 7 Jan 2022

Cited by 12 | Viewed by 2243

Abstract

There are massive landslides and potential landslides along the Three Rivers Basin in the Qinghai–Tibet Plateau, which pose a serious threat to the Sichuan–Tibet Railway. A normal shaking table model test was conducted to study the dynamic characteristics and dynamic response of a [...] Read more.

There are massive landslides and potential landslides along the Three Rivers Basin in the Qinghai–Tibet Plateau, which pose a serious threat to the Sichuan–Tibet Railway. A normal shaking table model test was conducted to study the dynamic characteristics and dynamic response of a symmetrical counter-bedding rock slope based on the Zongrong Village landslide. The influences of the dynamic parameters, seismic wave type, and a weak intercalated layer on the slope’s dynamic response were considered. The results showed symmetry between the growth trend of the acceleration amplification factor and other research results. When the input wave amplitude was constant, the acceleration amplification factor increased at first and then decreased as the frequency increased. When the input frequency was near the slope’s natural frequency, the acceleration amplification factor increased at first and then decreased with an increase in the input amplitude and reached the maximum value at 0.3 g. The acceleration amplification factor increased linearly with height in the vertical direction inside the slope but increased slowly at first and then sharply along the slope surface, reaching the maximum value at the slope’s top and exhibiting an obvious “elevation effect”. When sinusoidal waves, Wolong waves, and Maoxian waves with the same amplitude were input, the slope’s amplification effect on the bedrock wave was more obvious. The weak intercalated layer showed the phenomenon of “thin layer amplification” and “thick layer attenuation” in response to the input seismic wave. The slope’s failure process can be roughly divided into three stages: (1) the formation of tensile cracks at the top and shear cracks at the toe; (2) the extension of cracks and the sliding of the slope-surface block; (3) the formation of the main sliding surface. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 2767 KiB

Open AccessArticle

A Modified Van Der Pol Oscillator Model for the Unsteady Lift Produced by a Flapping Flat Plate for Different Positions of the Rotation Axis

by Chedhli Hafien and Abdellatif Messaoudi

Symmetry 2022, 14(1), 88; https://doi.org/10.3390/sym14010088 - 6 Jan 2022

Cited by 2 | Viewed by 2166

Abstract

To understand the nonlinear interaction between unsteady aerodynamic forces and the kinematics of structures, we theoretically and numerically investigated the characteristics of lift coefficients produced by a flapping thin flat plate controlled by the rotation axis position. The flat plate was placed in [...] Read more.

To understand the nonlinear interaction between unsteady aerodynamic forces and the kinematics of structures, we theoretically and numerically investigated the characteristics of lift coefficients produced by a flapping thin flat plate controlled by the rotation axis position. The flat plate was placed in a 2-D incompressible flow at a very low Reynolds number (Re = 300). We showed that the behavior of the unsteady aerodynamic forces suggests the existence of a limit cycle. In this context, we developed a Reduced Order Model (ROM) by resolving the modified van der Pol oscillator using the Taylor development method and computational fluid dynamics (CFD) solutions. A numerical solution was obtained by integrating the differential equation of the modified van der Pol oscillator using the fourth-order Runge–Kutta method (RK4). The model was validated by comparing this solution with the reformulated equation of the added mass lift coefficient. Using CFD and ROM solutions, we analyzed the dependency of the unsteady lift coefficient generation on the kinematics of the flapping flat plate. We showed that the evolution of the lift coefficient is influenced by the importance of the rotation motion of the Leading Edge (LE) or Trailing Edge (TE), according to the position of the rotation axis. Indeed, when the rotation axis is moved towards the LE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the TE and the rotation axis. However, when the rotation axis is moved towards the TE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the LE and the rotation axis. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 3129 KiB

Open AccessArticle

New Elements of Analysis of a Degenerate Chenciner Bifurcation

by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu

Symmetry 2022, 14(1), 77; https://doi.org/10.3390/sym14010077 - 5 Jan 2022

Cited by 2 | Viewed by 1912

Abstract

A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters

(α_{1}, α_{2}) \to (β_{1}, β_{2})

is [...] Read more.

A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters

(α_{1}, α_{2}) \to (β_{1}, β_{2})

is not longer regular at

(0, 0)

; therefore, implicit function theorem (IFT) cannot be applied around the origin, and a new transformation is necessary. The approach in this article to a case of Chenciner bifurcation is theoretical, but it can provide an answer for a number of applications of dynamical systems. We studied the bifurcation scenario and found out that, by this transformation, four different bifurcation diagrams are obtained, and the non-degenerate Chenciner bifurcation can be described by two bifurcation diagrams. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 2733 KiB

Open AccessArticle

Design and Stability Analysis of a Robust-Adaptive Sliding Mode Control Applied on a Robot Arm with Flexible Links

by Çağlar Uyulan

Vibration 2022, 5(1), 1-19; https://doi.org/10.3390/vibration5010001 - 30 Dec 2021

Cited by 5 | Viewed by 4278

Abstract

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. [...] Read more.

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. The main purpose of this paper was to propose a robust adaptive solution for stabilizing and tracking direct-drive (DD) flexible robot arms under parameter and model uncertainties, as well as external disturbances. A lightweight robot arm subject to external and internal dynamic effects was taken into consideration. The challenges were compensating actuator dynamics with the inverter switching effects and torque ripples, stabilizing the zero dynamics under parameter/model uncertainties and disturbances while precisely tracking the predefined reference position. The precise control of this kind of system demands an accurate system model and knowledge of all sources that excite unmodeled dynamics. For this purpose, equations of motion for a flexible robot arm were derived and formulated for the large motion via Lagrange’s method. The goals were determined to achieve high-speed, precise position control, and satisfied accuracy by compensating the unwanted torque ripple and friction that degrades performance through an adaptive robust control approach. The actuator dynamics and their effect on the torque output were investigated due to the transmitted torque to the load side. The high-performance goals, precision and robustness issues, and stability concerns were satisfied by using robust-adaptive input-output linearization-based control law combining chattering-free sliding mode control (SMC) while avoiding the excitation of unmodeled dynamics. The following highlights are covered: A 2-DOF flexible robot arm considering actuator dynamics was modelled; the theoretical implication of the chattering-free sliding mode-adaptive linearizing algorithm, which ensures robust stabilization and precise tracking control, was designed based on the full system model including actuator dynamics with computer simulations. Stability analysis of the zero dynamics originated from the Lyapunov theorem was performed. The conceptual design necessity of nonlinear observers for the estimation of immeasurable variables and parameters required for the control algorithms was emphasized. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 5190 KiB

Open AccessArticle

Full-Scale Measurements of Wind Characteristics on a High-Rise Building during Typhoon Sarika

by Jiaxing Hu, Zhengnong Li and Zhefei Zhao

Appl. Sci. 2022, 12(1), 324; https://doi.org/10.3390/app12010324 - 30 Dec 2021

Viewed by 1881

Abstract

A full-scale measurement of wind characteristics atop a high-rise building (with a height of 115 m) was conducted during the passage of Typhoon Sarika on 18 October 2016. Wind field characteristics, wind speed, and wind direction atop the building were recorded synchronously, and [...] Read more.

A full-scale measurement of wind characteristics atop a high-rise building (with a height of 115 m) was conducted during the passage of Typhoon Sarika on 18 October 2016. Wind field characteristics, wind speed, and wind direction atop the building were recorded synchronously, and turbulence intensity, turbulence integral scale, gust factor, and power spectrum were investigated. Meanwhile, the time and frequency domain characteristics of the wind field were analyzed. The stationarity test results of Typhoon Sarika at different time steps are researched in a runs test. And the time-frequency analysis of non-stationary samples of fluctuating wind speed are conducted by wavelet transform, the measured data are valuable for the wind-resistant design of high-rise buildings in typhoon-prone regions. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 6937 KiB

Open AccessArticle

Dynamic Response of Rock-like Materials Based on SHPB Pulse Waveform Characteristics

by Bi Sun, Rui Chen, Yang Ping, Zhende Zhu, Nan Wu and Yanxin He

Materials 2022, 15(1), 210; https://doi.org/10.3390/ma15010210 - 28 Dec 2021

Cited by 17 | Viewed by 2334

Abstract

Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in the split-Hopkinson pressure bar (SHPB) numerical simulation research. [...] Read more.

Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in the split-Hopkinson pressure bar (SHPB) numerical simulation research. In response to this problem, this paper discusses the effects of different pulse types and pulse waveforms on the incident waveform and dynamic response characteristics of specimens based on particle flow code (PFC). The research identifies a critical interval of rock dynamic strength, where the dynamic strength of the specimen is independent of the strain rate but increases with the amplitude of the incident stress wave. When the critical interval is exceeded, the dynamic strength is determined by the strain rate and strain rate gradient. The strain rate of the specimen is only related to the slope of the incident stress wave and is independent of its amplitude. It is also determined that the inertia effect cannot be eliminated in the SHPB. The slope of the velocity pulse waveform determines the strain rate of the specimen, the slope of the force pulse waveform determines the strain rate gradient of the specimen, and the upper bottom time determines the strain rate of the specimen. It provides a reference for SHPB numerical simulation. A dynamic strength prediction model of rock-like materials is then proposed, which considers the effects of strain rate and strain rate gradient. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 326 KiB

Open AccessArticle

Full Information H₂ Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

by Hongji Ma and Yang Wang

Mathematics 2022, 10(1), 37; https://doi.org/10.3390/math10010037 - 23 Dec 2021

Cited by 20 | Viewed by 2690

Abstract

This paper addresses an

H_{2}

optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence [...] Read more.

This paper addresses an

H_{2}

optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the

H_{2}

norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an

H_{2}

dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 12151 KiB

Open AccessArticle

Study on Influencing Factors of Helicopter Brownout Evolution Based on CFD-DEM

by Yihua Cao, Gaozhan Wang and Chongwen Jiang

Appl. Sci. 2022, 12(1), 126; https://doi.org/10.3390/app12010126 - 23 Dec 2021

Cited by 3 | Viewed by 3042

Abstract

The gas-solid two-phase flow model is constructed based on the Euler-Lagrangian framework. The

S S T k - ω

two-equation turbulence model and the soft ball model are coupled by computational fluid dynamics (CFD) and a discrete element model (DEM). Brownout is [...] Read more.

The gas-solid two-phase flow model is constructed based on the Euler-Lagrangian framework. The

S S T k - ω

two-equation turbulence model and the soft ball model are coupled by computational fluid dynamics (CFD) and a discrete element model (DEM). Brownout is then simulated by the above method with sliding mesh. As the calculation examples show, the simulations and experiments of the Lynx rotor and the Caradonna–Tung rotor are compared. The coupling method is verified through calculation of the rotor lift coefficient, blade section pressure coefficient and tip vortex shedding position. The results show that when the helicopter is hovering at a height of 0.52R from the ground, it will cause brownout and the pilot’s vision will be obscured by sand. When the hovering height is 1R, the phenomenon of brownout is not serious. The movement speed of most sand dust is about 12 m/s, and the height of the sand dust from the ground will gradually increase over time. Large particles of sand are more difficult to be entrained into the air than the small particles, and the particles with a radius of 50 um are basically accumulated on the ground. Moreover, the slotted-Tip rotor has an effect on restraining brownout. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 1996 KiB

Open AccessArticle

Investigations on the Control of COVID-19 and Suggestions for Re-Open Based on Model Study

by Yongxue Chen, Jiayu Shen, Shijing Li and Yongxian Wen

Mathematics 2022, 10(1), 22; https://doi.org/10.3390/math10010022 - 21 Dec 2021

Viewed by 2973

Abstract

Data-based analysis gives out an estimation of the incubation period. A dynamic model is established and discussed. Disease reproduction number reveals the high probability of COVID-19 pandemic, but strengthening the exposure of asymptomatic people will help to curb the transmission, and measures of [...] Read more.

Data-based analysis gives out an estimation of the incubation period. A dynamic model is established and discussed. Disease reproduction number reveals the high probability of COVID-19 pandemic, but strengthening the exposure of asymptomatic people will help to curb the transmission, and measures of contact-tracking and stay-at-home play a replaceable role. Discussions point out that social disruption can be avoided if the contact tracking rate can be more than 0.5. Investigations for re-opening show that a city of the same size as Wuhan can be reopened if new cases are continuously below 1000 for a few days and when they are less than 500, with the assurance of contact tracking associated with extensive testing. In short, tracking and testing are the prioritized strategies, while maintaining awareness can shorten the epidemic period and mobility restrictions can be avoided. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 3923 KiB

Open AccessArticle

Attention Optimized Deep Generative Adversarial Network for Removing Uneven Dense Haze

by Wenxuan Zhao, Yaqin Zhao, Liqi Feng and Jiaxi Tang

Symmetry 2022, 14(1), 1; https://doi.org/10.3390/sym14010001 - 21 Dec 2021

Cited by 10 | Viewed by 2907

Abstract

The existing dehazing algorithms are problematic because of dense haze being unevenly distributed on the images, and the deep convolutional dehazing network relying too greatly on large-scale datasets. To solve these problems, this paper proposes a generative adversarial network based on the deep [...] Read more.

The existing dehazing algorithms are problematic because of dense haze being unevenly distributed on the images, and the deep convolutional dehazing network relying too greatly on large-scale datasets. To solve these problems, this paper proposes a generative adversarial network based on the deep symmetric Encoder-Decoder architecture for removing dense haze. To restore the clear image, a four-layer down-sampling encoder is constructed to extract the semantic information lost due to the dense haze. At the same time, in the symmetric decoder module, an attention mechanism is introduced to adaptively assign weights to different pixels and channels, so as to deal with the uneven distribution of haze. Finally, the framework of the generative adversarial network is generated so that the model achieves a better training effect on small-scale datasets. The experimental results showed that the proposed dehazing network can not only effectively remove the unevenly distributed dense haze in the real scene image, but also achieve great performance in real-scene datasets with less training samples, and the evaluation indexes are better than other widely used contrast algorithms. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 2924 KiB

Open AccessArticle

Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes

by Yanli Chen, Lei Wang and Xiaosong Yang

Mathematics 2021, 9(24), 3285; https://doi.org/10.3390/math9243285 - 17 Dec 2021

Viewed by 2253

Abstract

The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine systems with two switching planes regardless of [...] Read more.

The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine systems with two switching planes regardless of the symmetry. An analytic proof is provided using the concrete expression forms of the analytic solution, stable manifold, and unstable manifold. Meanwhile, a sufficient condition for the existence of two homoclinic orbits is also obtained. Furthermore, two concrete piecewise affine asymmetric systems with two homoclinic orbits have been constructed successfully, demonstrating the method’s effectiveness. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 433 KiB

Open AccessArticle

A Novel Model for Distributed Denial of Service Attack Analysis and Interactivity

by Ashraf Ahmad, Yousef AbuHour and Firas Alghanim

Symmetry 2021, 13(12), 2443; https://doi.org/10.3390/sym13122443 - 17 Dec 2021

Cited by 2 | Viewed by 3225

Abstract

A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots [...] Read more.

A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots throughout the network. A mathematical differential equation model is proposed to represent the dynamism of nodes at different compartments of the model. The model considers two levels of security, with the assumption that the recovered nodes do not return to the same security level. In previous models, the recovered nodes are returned to be suspect on the same security level, which is an unrealistic assumption. Moreover, it is assumed that the attacker can use the infected target nodes to attack again. With such epidemic-like assumptions of infection, different cases are presented and discussed, and the stability of the model is analyzed as well; reversing the symmetry transformation of attacking nodes population is also proven. The proposed model has many parameters in order to precisely describe the infection movement and propagation. Numerical simulation methods are used to solve the developed system of equations using MATLAB, with the intention of finding the best counteraction to control DDoS spread throughout a network. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 6103 KiB

Open AccessArticle

Hybrid Sliding Mode Control of Full-Car Semi-Active Suspension Systems

by Ayman Aljarbouh, Muhammad Fayaz, Muhammad Shuaib Qureshi and Younes Boujoudar

Symmetry 2021, 13(12), 2442; https://doi.org/10.3390/sym13122442 - 17 Dec 2021

Cited by 17 | Viewed by 4389

Abstract

With the advance in technology in driving vehicles, there is currently more emphasis on developing advanced control systems for better road handling stability and ride comfort. However, one of the challenging problems in the design and implementation of intelligent suspension systems is that [...] Read more.

With the advance in technology in driving vehicles, there is currently more emphasis on developing advanced control systems for better road handling stability and ride comfort. However, one of the challenging problems in the design and implementation of intelligent suspension systems is that there is currently no solution supporting the export of generic suspension models and control components for integration into embedded Electronic Control Units (ECUs). This significantly limits the usage of embedded suspension components in automotive production code software as it requires very high efforts in implementation, manual testing, and fulfilling coding requirements. This paper introduces a new dynamic model of full-car suspension system with semi-active suspension behavior and provides a hybrid sliding mode approach for control of full-car suspension dynamics such that the road handling stability and ride comfort characteristics are ensured. The semi-active suspension model and the hybrid sliding mode controller are implemented as Functional Mock-Up Units (FMUs) conforming to the Functional Mock-Up Interface for embedded systems (eFMI) and are calibrated with a set experimental tests using a 1/5 Soben-car test bench. The methods and prototype implementation proposed in this paper allow both model and controller re-usability and provide a generic way of integrating models and control software into embedded ECUs. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 356 KiB

Open AccessArticle

Continuity and Analyticity for the Generalized Benjamin–Ono Equation

by Xiaolin Pan, Bin Wang and Rong Chen

Symmetry 2021, 13(12), 2435; https://doi.org/10.3390/sym13122435 - 16 Dec 2021

Viewed by 2223

Abstract

This work mainly focuses on the continuity and analyticity for the generalized Benjamin–Ono (g-BO) equation. From the local well-posedness results for g-BO equation, we know that its solutions depend continuously on their initial data. In the present paper, we further show that such [...] Read more.

This work mainly focuses on the continuity and analyticity for the generalized Benjamin–Ono (g-BO) equation. From the local well-posedness results for g-BO equation, we know that its solutions depend continuously on their initial data. In the present paper, we further show that such dependence is not uniformly continuous in Sobolev spaces

H^{s} (R)

with

s > 3 / 2

. We also provide more information about the stability of the data-solution map, i.e., the solution map for g-BO equation is Hölder continuous in

H^{r}

-topology for all

0 \leq r < s

with exponent

α

depending on s and r. Finally, applying the generalized Ovsyannikov type theorem and the basic properties of Sobolev–Gevrey spaces, we prove the Gevrey regularity and analyticity for the g-BO equation. In addition, by the symmetry of the spatial variable, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 282 KiB

Open AccessArticle

An Implicit Hybrid Delay Functional Integral Equation: Existence of Integrable Solutions and Continuous Dependence

by Ahmed M. A. El-Sayed, Hind H. G. Hashem and Shorouk M. Al-Issa

Mathematics 2021, 9(24), 3234; https://doi.org/10.3390/math9243234 - 14 Dec 2021

Cited by 9 | Viewed by 2171

Abstract

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness [...] Read more.

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

20 pages, 4803 KiB

Open AccessArticle

A Study on Nonlinear Dynamic Response of the Large-Span Roof Structure with Suspended Substructure

by Rui Pan, Baofeng Zheng and Ying Qin

Symmetry 2021, 13(12), 2397; https://doi.org/10.3390/sym13122397 - 12 Dec 2021

Cited by 1 | Viewed by 2507

Abstract

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on [...] Read more.

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 3745 KiB

Open AccessArticle

The Study of Generalized Synchronization between Two Identical Neurons Based on the Laplace Transform Method

by Bin Zhen and Ran Liu

Appl. Sci. 2021, 11(24), 11774; https://doi.org/10.3390/app112411774 - 11 Dec 2021

Cited by 1 | Viewed by 2182

Abstract

In this paper, a new method is proposed based on the auxiliary system approach to investigate generalized synchronization between two identical neurons with unidirectional coupling. Different from other studies, the synchronization error system between the response and auxiliary systems is converted into a [...] Read more.

In this paper, a new method is proposed based on the auxiliary system approach to investigate generalized synchronization between two identical neurons with unidirectional coupling. Different from other studies, the synchronization error system between the response and auxiliary systems is converted into a set of Volterra integral equations according to the Laplace transform method and convolution theorem. By using the successive approximation method in the theory of integral equations, an analytical criterion for the detection of generalized synchronization between two identical neurons is obtained. It is found that there is a time difference between two signals of neurons when the generalized synchronization between them is achieved. Furthermore, the value of the time difference has no relation to the generalized synchronization condition but depends on the coupling function between two neurons. The study in this paper shows that one can construct a coupling function between two identical neurons using the current signal of the drive system to predict its future signal or make its past signal reappear. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 2224 KiB

Open AccessArticle

A Lyapunov-Based Optimal Integral Finite-Time Tracking Control Approach for Asymmetric Nonholonomic Robotic Systems

by Khalid A. Alattas, Saleh Mobayen, Wudhichai Assawinchaichote, Jihad H. Asad, Jan Awrejcewicz, Ayman A. Aly and Abdulaziz H. Alghtani

Symmetry 2021, 13(12), 2367; https://doi.org/10.3390/sym13122367 - 8 Dec 2021

Cited by 4 | Viewed by 2666

Abstract

This study suggests a control Lyapunov-based optimal integral terminal sliding mode control (ITSMC) technique for tracker design of asymmetric nonholonomic robotic systems in the existence of external disturbances. The design procedure is based on the control Lyapunov function (CLF) approach. Hence, the output [...] Read more.

This study suggests a control Lyapunov-based optimal integral terminal sliding mode control (ITSMC) technique for tracker design of asymmetric nonholonomic robotic systems in the existence of external disturbances. The design procedure is based on the control Lyapunov function (CLF) approach. Hence, the output tracking problem is solved by combining the ITSMC with optimal control. The CLF synthesizes a nonlinear optimal control input for the nominal system. Once the control system’s states lie far away from the operating point, it is activated to drive them toward the equilibrium point optimally. However, on the condition that the system perturbations are the main factor, the ITSMC would be designed to take over in the vicinity of the equilibrium point. Accordingly, the control goals, such as robustness and precise control, are warranted in the perturbed system. The usefulness of the suggested method is demonstrated with a wheeled mobile robot via a simulation study. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 443 KiB

Open AccessArticle

Functional Effects of Permeability on Oldroyd-B Fluid under Magnetization: A Comparison of Slipping and Non-Slipping Solutions

by Muhammad Bilal Riaz, Jan Awrejcewicz and Aziz Ur Rehman

Appl. Sci. 2021, 11(23), 11477; https://doi.org/10.3390/app112311477 - 3 Dec 2021

Cited by 16 | Viewed by 1978

Abstract

In this article, the impact of Newtonian heating in addition to slip effects was critically examined on the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely vertical plate. The functional effects such as the retardation and relaxation of materials can [...] Read more.

In this article, the impact of Newtonian heating in addition to slip effects was critically examined on the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely vertical plate. The functional effects such as the retardation and relaxation of materials can be estimated for magnetized permeability based on the relative decrease or increase during magnetization. From this perspective, a new mathematical model was formulated based on non-slippage and slippage postulates for the Oldroyd-B fluid with magnetized permeability. The heat transfer induction was also examined through a non-fractional developed mathematical model for the Oldroyd-B fluid. The exact solution expressions for non-dimensional equations of velocity and temperature were explored by employing Laplace integral transformation under slipping boundary conditions under Newtonian heating. The heat transfer rate was estimated through physical interpretation by considering the limits on the solutions induced by the Nusselt number. To comprehensively discuss the dynamics of the considered problem, the physical impacts of different parameters were studied and reverberations were graphically highlighted and deliberated. Furthermore, in order to validate the results, two limiting models, namely the Maxwell model and the second grade model, were used to compare the relevant flow characteristics. Additionally, in order to perform the parametric analysis, the graphical representation was portrayed for non-slipping and slipping solutions for velocity and temperature. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 449 KiB

Open AccessArticle

Relation Selective Graph Convolutional Network for Skeleton-Based Action Recognition

by Wenjie Yang, Jianlin Zhang, Jingju Cai and Zhiyong Xu

Symmetry 2021, 13(12), 2275; https://doi.org/10.3390/sym13122275 - 30 Nov 2021

Cited by 6 | Viewed by 2447

Abstract

Graph convolutional networks (GCNs) have made significant progress in the skeletal action recognition task. However, the graphs constructed by these methods are too densely connected, and the same graphs are used repeatedly among channels. Redundant connections will blur the useful interdependencies of joints, [...] Read more.

Graph convolutional networks (GCNs) have made significant progress in the skeletal action recognition task. However, the graphs constructed by these methods are too densely connected, and the same graphs are used repeatedly among channels. Redundant connections will blur the useful interdependencies of joints, and the overly repetitive graphs among channels cannot handle changes in joint relations between different actions. In this work, we propose a novel relation selective graph convolutional network (RS-GCN). We also design a trainable relation selection mechanism. It encourages the model to choose solid edges to work and build a stable and sparse topology of joints. The channel-wise graph convolution and multiscale temporal convolution are proposed to strengthening the model’s representative power. Furthermore, we introduce an asymmetrical module named the spatial-temporal attention module for more stable context modeling. Combining those changes, our model achieves state-of-the-art performance on three public benchmarks, namely NTU-RGB+D, NTU-RGB+D 120, and Northwestern-UCLA. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 13347 KiB

Open AccessArticle

A Numerical Study of the Wind Speed Effect on the Flow and Acoustic Characteristics of the Minor Cavity Structures in a Two-Wheel Landing Gear

by Longlong Huang, Kun Zhao, Junbiao Liang, Victor Kopiev, Ivan Belyaev and Tian Zhang

Appl. Sci. 2021, 11(23), 11235; https://doi.org/10.3390/app112311235 - 26 Nov 2021

Cited by 5 | Viewed by 2297

Abstract

The landing gear is widely concerned as the main noise source of airframe noise. The flow characteristics and aerodynamic noise characteristics of the landing gear were numerically simulated based on Large Eddy Simulation and Linearized Euler Equation, and the feasibility of the simulation [...] Read more.

The landing gear is widely concerned as the main noise source of airframe noise. The flow characteristics and aerodynamic noise characteristics of the landing gear were numerically simulated based on Large Eddy Simulation and Linearized Euler Equation, and the feasibility of the simulation model was verified by experiments. Then the wind speed effect on the flow and acoustic characteristics of the minor cavity structures in a two-wheel landing gear were analyzed. The results show that the interaction of vortices increases with the increase of velocity at the brake disc, resulting in a slight increase in the amplitude of pressure fluctuation at 55 m·s⁻¹~75 m·s⁻¹. With the increase of speed, the obstruction at the lower hole of torque link decreases, and many vortical structures flow out of the lower hole and are dissipated, so that the pressure fluctuation amplitude of 75 m·s⁻¹ almost does not increase relative to 55 m·s⁻¹. The contribution of each part in the landing gear to the overall noise is as follows: shock strut > tire > torque link > brake disc. At the speed of 34 m·s⁻¹~55 m·s⁻¹, the contribution of each component to the total noise increases with the increase of speed, and the small components such as torque link and brake disc contribute more to the total noise. At the speed of 55 m·s⁻¹~75 m·s⁻¹, the increase of overall noise mainly comes from the main components such as shock strut and tire, and the brake disc and torque link contribute very little to the overall noise. It provides a reference for the further noise reduction optimization design of the landing gear. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 329 KiB

Open AccessArticle

Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean

c_{0} (N)

Space

by Farrukh Mukhamedov, Otabek Khakimov and Abdessatar Souissi

Mathematics 2021, 9(22), 2986; https://doi.org/10.3390/math9222986 - 22 Nov 2021

Cited by 3 | Viewed by 2346

Abstract

In the present paper, we propose to study generalized weighted backward shifts

B_{B}

over non-Archimedean

c_{0} (N)

spaces; here,

B = (b_{i j})

is an upper triangular matrix with [...] Read more.

In the present paper, we propose to study generalized weighted backward shifts

B_{B}

over non-Archimedean

c_{0} (N)

spaces; here,

B = (b_{i j})

is an upper triangular matrix with

{sup}_{i, j} | b_{i j} | < \infty

. We investigate the sypercyclic and hypercyclic properties of

B_{B}

. Furthermore, certain properties of the operator

I + B_{B}

are studied as well. To establish the hypercyclic property of

I + B_{B}

we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

31 pages, 890 KiB

Open AccessArticle

Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

by Ahmed A. El-Deeb and Jan Awrejcewicz

Mathematics 2021, 9(22), 2964; https://doi.org/10.3390/math9222964 - 20 Nov 2021

Cited by 11 | Viewed by 1778

Abstract

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the [...] Read more.

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the

(γ, a)

-nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

24 pages, 12362 KiB

Open AccessArticle

The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

by Xin Yang, Guangjun Zhang, Xueren Li and Dong Wang

Symmetry 2021, 13(11), 2204; https://doi.org/10.3390/sym13112204 - 18 Nov 2021

Cited by 5 | Viewed by 2064

Abstract

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. [...] Read more.

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order

q

and the feedback gain parameter

k_{1}

. In addition, the fractional-order or the parameter

k_{1}

can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by

q

or parameter

k_{1}

are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter

β

of the electromagnetic radiation,

k_{1}

and

q

, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of

k_{1}

and

q

can be summarized into three cases:

β > 0.02

,

- 0.06 < β < 0.02

and

β < - 0.06

. The influence rules and some interesting phenomena are investigated. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 1376 KiB

Open AccessArticle

Three-Phase Feeder Load Balancing Based Optimized Neural Network Using Smart Meters

by Lina Alhmoud, Qosai Nawafleh and Waled Merrji

Symmetry 2021, 13(11), 2195; https://doi.org/10.3390/sym13112195 - 17 Nov 2021

Cited by 9 | Viewed by 4136

Abstract

The electricity distribution system is the coupling point between the utility and the end-user. Typically, these systems have unbalanced feeders due to the variety of customers’ behaviors. Some significant problems occur; the unbalanced loads increase the operational cost and system investment. In radial [...] Read more.

The electricity distribution system is the coupling point between the utility and the end-user. Typically, these systems have unbalanced feeders due to the variety of customers’ behaviors. Some significant problems occur; the unbalanced loads increase the operational cost and system investment. In radial distribution systems, swapping loads between the three phases is the most effective method for phase balancing. It is performed manually and subjected to load flow equations, capacity, and voltage constraints. Recently, due to smart grids and automated networks, dynamic phase balancing received more attention, thus swapping the loads between the three phases automatically when unbalance exceeds permissible limits by using a remote-controlled phase switch selector/controller. Automatic feeder reconfiguration and phase balancing eliminates the service interruption, enhances energy restoration, and minimize losses. In this paper, a case study from the Irbid district electricity company (IDECO) is presented. Optimal reconfiguration of phase balancing using three techniques: feed-forward back-propagation neural network (FFBPNN), radial basis function neural network (RBFNN), and a hybrid are proposed to control the switching sequence for each connected load. The comparison shows that the hybrid technique yields the best performance. This work is simulated using MATLAB and C programming language. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 3030 KiB

Open AccessArticle

Sign Stability of Dual Switching Linear Continuous-Time Positive Systems

by Liang Liu, Fei Long, Lipo Mo and Qianqian Mu

Symmetry 2021, 13(11), 2194; https://doi.org/10.3390/sym13112194 - 17 Nov 2021

Cited by 2 | Viewed by 1761

Abstract

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but [...] Read more.

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

35 pages, 9626 KiB

Open AccessArticle

Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

by Sabry M. El-Shourbagy, Nasser A. Saeed, Magdi Kamel, Kamal R. Raslan, Mohamed K. Aboudaif and Jan Awrejcewicz

Appl. Sci. 2021, 11(22), 10839; https://doi.org/10.3390/app112210839 - 16 Nov 2021

Cited by 28 | Viewed by 2878

Abstract

The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many [...] Read more.

The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many advantages over the eight-pole one (such as a negligible cross-coupling effect, low power consumption, better suspension behaviors, and high dynamic stiffness), the twelve-pole system oscillatory behaviors have not been studied before. Therefore, this article is assigned to explore the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller for the first time. The normalized equations of motion that govern the system vibrations are established by means of classical mechanics. Then, the averaging equations are extracted utilizing the asymptotic analysis. The influence of all system parameters on the steady-state oscillation amplitudes is explored. Stability charts in a two-dimensional space are constructed. The stable margin of both the system and control parameters is determined. The obtained investigations reveal that proportional gain plays a dominant role in reshaping the dynamics and motion bifurcation of the twelve-pole systems. In addition, it is found that stability charts of the system can be controlled by simply utilizing both the proportional and derivative gains. Moreover, the numerical simulations showed that the twelve-poles system can exhibit both quasiperiodic and chaotic oscillations besides the periodic motion depending on the control parameters’ magnitude. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 422 KiB

Open AccessArticle

An Eco-Epidemiological Model Incorporating Harvesting Factors

by Kawa Hassan, Arkan Mustafa and Mudhafar Hama

Symmetry 2021, 13(11), 2179; https://doi.org/10.3390/sym13112179 - 15 Nov 2021

Cited by 7 | Viewed by 2700

Abstract

The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. [...] Read more.

The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 4221 KiB

Open AccessArticle

Deep Convolutional Neural Networks for Tea Tree Pest Recognition and Diagnosis

by Jing Chen, Qi Liu and Lingwang Gao

Symmetry 2021, 13(11), 2140; https://doi.org/10.3390/sym13112140 - 10 Nov 2021

Cited by 15 | Viewed by 2789

Abstract

Due to the benefits of convolutional neural networks (CNNs) in image classification, they have been extensively used in the computerized classification and focus of crop pests. The intention of the current find out about is to advance a deep convolutional neural network to [...] Read more.

Due to the benefits of convolutional neural networks (CNNs) in image classification, they have been extensively used in the computerized classification and focus of crop pests. The intention of the current find out about is to advance a deep convolutional neural network to mechanically identify 14 species of tea pests that possess symmetry properties. (1) As there are not enough tea pests images in the network to train the deep convolutional neural network, we proposes to classify tea pests images by fine-tuning the VGGNET-16 deep convolutional neural network. (2) Through comparison with traditional machine learning algorithms Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP), the performance of our method is evaluated (3) The three methods can identify tea tree pests well: the proposed convolutional neural network classification has accuracy up to 97.75%, while MLP and SVM have accuracies of 76.07% and 68.81%, respectively. Our proposed method performs the best of the assessed recognition algorithms. The experimental results also show that the fine-tuning method is a very powerful and efficient tool for small datasets in practical problems. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 365 KiB

Open AccessArticle

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

by Kamil Borawski

Appl. Sci. 2021, 11(22), 10568; https://doi.org/10.3390/app112210568 - 10 Nov 2021

Cited by 4 | Viewed by 2003

Abstract

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of [...] Read more.

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used to show the efficacy of the presented approach. Our considerations were based on the Drazin inverse matrix method. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 274 KiB

Open AccessArticle

Existence Solution for Coupled System of Langevin Fractional Differential Equations of Caputo Type with Riemann–Stieltjes Integral Boundary Conditions

by Ahmed Salem and Lamya Almaghamsi

Symmetry 2021, 13(11), 2123; https://doi.org/10.3390/sym13112123 - 8 Nov 2021

Cited by 17 | Viewed by 2250

Abstract

By employing Shauder fixed-point theorem, this work tries to obtain the existence results for the solution of a nonlinear Langevin coupled system of fractional order whose nonlinear terms depend on Caputo fractional derivatives. We study this system subject to Stieltjes integral boundary conditions. [...] Read more.

By employing Shauder fixed-point theorem, this work tries to obtain the existence results for the solution of a nonlinear Langevin coupled system of fractional order whose nonlinear terms depend on Caputo fractional derivatives. We study this system subject to Stieltjes integral boundary conditions. A numerical example explaining our result is attached. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

22 pages, 648 KiB

Open AccessArticle

ACTS: An Ant Colony Based Transmission Scheduling Approach for Cloud Network Collaboration Environment

by Ruiying Cheng, Pan Zhang, Lei Xie, Yongqi Ai and Peng Xu

Symmetry 2021, 13(11), 2109; https://doi.org/10.3390/sym13112109 - 6 Nov 2021

Cited by 2 | Viewed by 1897

Abstract

In traditional cloud computing research, it is often considered that the network resources between edge devices and cloud platform are sufficient, and the symmetry between the upward link from edge devices to the cloud platform and the downward link from cloud platform to [...] Read more.

In traditional cloud computing research, it is often considered that the network resources between edge devices and cloud platform are sufficient, and the symmetry between the upward link from edge devices to the cloud platform and the downward link from cloud platform to edge devices is definite. However, in many application scenarios, the network resources between edge devices and cloud platform might be limited, and the link symmetry may not be guaranteed. To solve this problem, network relay nodes are introduced to realize the data transmission between edge devices and the cloud platform. The environment in which network relay nodes that can cooperate with the cloud platform is called cloud network collaborative environment (CNCE). In CNCE, how to optimize data transmission from edge devices to cloud platform through relay nodes has become one of the most important research topics. In this paper, we focus on the following two influencing factors that previous studies ignored: (1) the multi-link and multi-constraint transmission process; and (2) the timely resource state of the relay node. Taking these factors into consideration, we design a novel data transmission scheduling algorithm, called ant colony based transmission scheduling approach (ACTS). First, we propose a multi-link optimization mechanism to optimize the constraint limits. This mechanism divides the transmission into two links called the downlink relay link and uplink relay link. For the downlink relay link, we use the store-and-forward method for the optimization. For the uplink relay link, we use the min–min method for the optimization. We use the ant colony algorithm for the overall optimization of the two links. Finally, we improve the pheromone update rule of the ant colony algorithm to avoid the algorithm from falling into a local optimum. Extensive experiments demonstrate that our proposed approach has better results in transmission efficiency than other advanced algorithms. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 4358 KiB

Open AccessArticle

Five-Year Performance of an ESE Lightning Protection System for a Large Scale PV Power Plant in Thailand

by Rungphet Kongnok, Thanakorn Pummaitong and Boonyang Plangklang

Symmetry 2021, 13(11), 2106; https://doi.org/10.3390/sym13112106 - 6 Nov 2021

Cited by 6 | Viewed by 7187

Abstract

This article presents a five-year performance review of an early streamer emission (ESE) air terminal lightning protection system for a large scale PV power plant in Thailand. The comparison effect of a Franklin lightning protection system and the ESE lightning protection system was [...] Read more.

This article presents a five-year performance review of an early streamer emission (ESE) air terminal lightning protection system for a large scale PV power plant in Thailand. The comparison effect of a Franklin lightning protection system and the ESE lightning protection system was analyzed for the PV power plant. The ESE lightning protection system was selected to be implemented in the PV power plant. The capacity of the PV power plant studied was 8 MWp on an area of 150,000 square meters in the Nong Ya Plong district, Phetchaburi province, Western Thailand. A Franklin lightning rod type was also designed to be implemented in this PV power plant. The Franklin lightning rod type comprised 122 pieces but the ESE lightning rod type consisted of only 11 pieces. The conceptual design of the Franklin rod type followed the standard of the Council of Engineers, Thailand, and the ESE lightning rod type followed the NFC17102 standard of France. The estimated cost of installation was a key comparison to select the lightning protection system; the total installation cost of the Franklin lightning rod type was USD 197,363.80 and the ESE lightning rod type was USD 44,338.06. The lightning system was applied to the lightning arrester in the power plant to provide good protection, in which the balance of the pole to the mounting position is required to optimize the system performance. The result of the simulation also showed that the shading effects of the Franklin rod type were greater than the ESE rod type. The installation cost of the Franklin lightning rod type was 4.45 times more expensive than the ESE lightning rod type. Therefore, the ESE lightning protection system was selected to be implemented in the PV power plant. From the recorded data of the five-year performance of the ESE lightning protection system (2016–2020), there were three occurrences of a lightning strike on the PV power plant. The ESE lightning protection system effectively protected and prevented the lightning strike to the PV power plant. This study can help and support with the selection of a lightning system for the protection of large scale PV power plants in the future. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 814 KiB

Open AccessArticle

Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst

by Vivek Mani Tripathi, Hari Mohan Srivastava, Harendra Singh, Chetan Swarup and Sudhanshu Aggarwal

Appl. Sci. 2021, 11(21), 10423; https://doi.org/10.3390/app112110423 - 5 Nov 2021

Cited by 15 | Viewed by 2681

Abstract

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at

the time t = 0

. The main objective of this paper is [...] Read more.

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at

the time t = 0

. The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 660 KiB

Open AccessArticle

Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model

by Wen Liu and Jianfeng Feng

Mathematics 2021, 9(21), 2776; https://doi.org/10.3390/math9212776 - 2 Nov 2021

Cited by 3 | Viewed by 2045

Abstract

In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the [...] Read more.

In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the mean-square stability matrix can be calculated from the Kronecker product, so as to compute three indicators (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the response to perturbation for the studied ecosystem. Since the above-measured amounts cannot be obtained explicitly, we use numerical simulation to draw the changing figures within the appropriate parameter range. Then we obtain some conclusions by comparing the numerical results. When perturbing any populations, increasing the disturbance intensity will reduce the mean-square stable area of the system. Ecologists can manage the ecosystem, reduce losses and maximize benefits according to the numerical results of the root-mean-square amplification envelope. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

31 pages, 78405 KiB

Open AccessArticle

On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

by Sabry M. El-Shourbagy, Nasser A. Saeed, Magdi Kamel, Kamal R. Raslan, Emad Abouel Nasr and Jan Awrejcewicz

Symmetry 2021, 13(11), 2069; https://doi.org/10.3390/sym13112069 - 2 Nov 2021

Cited by 13 | Viewed by 2403

Abstract

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system [...] Read more.

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 782 KiB

Open AccessArticle

New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales

by Ahmed A. El-Deeb, Hijaz Ahmad and Jan Awrejcewicz

Symmetry 2021, 13(11), 2049; https://doi.org/10.3390/sym13112049 - 31 Oct 2021

Cited by 1 | Viewed by 1595

Abstract

Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new

α

-conformable dynamic inequalities of Steffensen-type on time scales. In the case when

α = 1

, we obtain some [...] Read more.

Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new

α

-conformable dynamic inequalities of Steffensen-type on time scales. In the case when

α = 1

, we obtain some well-known time scale inequalities due to Steffensen inequalities. For some specific time scales, we further show some relevant inequalities as special cases:

α

-conformable integral inequalities and

α

-conformable discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

17 pages, 9390 KiB

Open AccessArticle

Dynamic Characteristics Analysis of Gear-Bearing System Considering Dynamic Wear with Flash Temperature

by Jinchi Xu, Xiaopeng Li, Renzhen Chen, Linlin Wang, Zemin Yang and Hexu Yang

Mathematics 2021, 9(21), 2739; https://doi.org/10.3390/math9212739 - 28 Oct 2021

Cited by 4 | Viewed by 2804

Abstract

The influence of the dynamic wear model considering the tooth contact flash temperature on the dynamic characteristics of a gear-bearing system is studied. Firstly, the meshing stiffness model, based on flash temperature theory, is established. Then, the changing of tooth surface temperature and [...] Read more.

The influence of the dynamic wear model considering the tooth contact flash temperature on the dynamic characteristics of a gear-bearing system is studied. Firstly, the meshing stiffness model, based on flash temperature theory, is established. Then, the changing of tooth surface temperature and meshing stiffness in the process of gear meshing is analyzed. Next, the initial tooth surface wear is calculated based on the Archard theory, and the dynamic wear model of the system is established. Finally, the effects of initial wear, friction factors, and damping ratio on the system response are studied. The results show that with the increase of fractal dimension D, the uncertainty and the fluctuation amplitude of backlash decrease, and the meshing force decreases. Therefore, the initial tooth surface wear is reduced, and the stability of the system response with a dynamic wear model is improved; with the increase of the friction coefficient, the tooth surface flash temperature rises, and the root mean square value of the vibration displacement of the system amplifies, which indicates that the system tends to be unstable; with the increase of damping ratio, the system changes from unstable quasi-periodic and chaotic motion to the stable periodic motion. The increase of damping accelerates the energy loss of the system and makes the system prone to be stable. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 3852 KiB

Open AccessArticle

Dislocation Topological Evolution and Energy Analysis in Misfit Hardening of Spherical Precipitate by the Parametric Dislocation Dynamics Simulation

by Haiwei Zheng, Jianbin Liu and Shinji Muraishi

Materials 2021, 14(21), 6368; https://doi.org/10.3390/ma14216368 - 25 Oct 2021

Cited by 3 | Viewed by 2082

Abstract

Interaction of a single dislocation line and a misfit spherical precipitate has been simulated by the Parametric Dislocation Dynamics (PDD) method in this research. The internal stress inside the precipitate is deduced from Eshelby’s inclusion theory, the stress of the dislocation line and [...] Read more.

Interaction of a single dislocation line and a misfit spherical precipitate has been simulated by the Parametric Dislocation Dynamics (PDD) method in this research. The internal stress inside the precipitate is deduced from Eshelby’s inclusion theory, the stress of the dislocation line and outside the precipitate is calculated by Green’s function. The influence of different relative heights of the primary slip plane on dislocation evolution is investigated, while the cross-slip mechanism and annihilation reaction are considered. The simulation results show three kinds of dislocation topological evolution: loop-forming (Orowan loop or prismatic loop), helix-forming, and gradual unpinning. The dislocation nodal force and the velocity vectors are visualized to study dislocation motion tendency. According to the stress–strain curve and the energy curves associated with the dislocation motion, the pinning stress level is strongly influenced by the topological change of dislocation as well as the relative heights of the primary slip plane. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 3326 KiB

Open AccessArticle

Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems

by Chih-Hsueh Lin, Chia-Wei Ho, Guo-Hsin Hu, Baswanth Sreeramaneni and Jun-Juh Yan

Mathematics 2021, 9(21), 2658; https://doi.org/10.3390/math9212658 - 21 Oct 2021

Cited by 7 | Viewed by 2004

Abstract

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of [...] Read more.

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of unified chaotic systems. Then, the secret message embedded in the master chaotic system can be transmitted from transmitter to receiver. Different from previous works using discontinuous SMC, the undesired chattering phenomenon can be fully eliminated, and it becomes possible to precisely recover the embedded secret message at the receiver. Last, an example is given to illustrate the success of secure data transmission with the continuous SMC developed in this paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 7305 KiB

Open AccessArticle

DFT Insights into the Hydrodenitrogenation and Ring-Opening of Indole on an M (M = Ni, Pt, Ni–Pt) Slab Model

by Cuiping Wang, Jinpeng Chu, Lianji Zhang, Yan Huang, Zhiqiang Zhang, Hao Chen and Hongqi Shi

Symmetry 2021, 13(10), 1950; https://doi.org/10.3390/sym13101950 - 16 Oct 2021

Cited by 1 | Viewed by 2230

Abstract

Density functional theory (DFT) calculation has been used to study the hydrodenitrogenation (HDN) and ring-opening of indole on an M (M = Ni, Pt, Ni–Pt) slab surface. The possible reaction pathway of indole hydrogenation has been investigated in order to reveal the bimetallic [...] Read more.

Density functional theory (DFT) calculation has been used to study the hydrodenitrogenation (HDN) and ring-opening of indole on an M (M = Ni, Pt, Ni–Pt) slab surface. The possible reaction pathway of indole hydrogenation has been investigated in order to reveal the bimetallic synergistic effects of an M slab surface. Compared to the mechanism of indole hydrogenation on an M slab surface, it was found that a PtNi(111) surface favors indole hydrogenation. According to the results of DFT calculation, it suggests that the bimetallic effect of the M surface plays an important role in indole hydrogenation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 29207 KiB

Open AccessArticle

An Integrated Spatio-Temporal Features Analysis Approach for Ocean Turbulence Using an Autonomous Vertical Profiler

by Xiuyan Liu, Dalei Song, Hua Yang, Xiaofeng Wang and Yunli Nie

Appl. Sci. 2021, 11(20), 9455; https://doi.org/10.3390/app11209455 - 12 Oct 2021

Cited by 3 | Viewed by 1825

Abstract

Turbulent energy cascade and intermittency are very important characteristics in the turbulent energy evolution process. However, understanding the temporal–spatial features of kinetic energy transfer and quantifying the correlations between different scales of turbulent energy remains an outstanding challenge. To deeply understand the spatial–temporal [...] Read more.

Turbulent energy cascade and intermittency are very important characteristics in the turbulent energy evolution process. However, understanding the temporal–spatial features of kinetic energy transfer and quantifying the correlations between different scales of turbulent energy remains an outstanding challenge. To deeply understand the spatial–temporal features in the energy transfer process, an integrated features identification and extraction method is proposed to quantitatively investigate the correlations using the ocean shear turbulence measured by an autonomous vertical reciprocating profiler (AVRP). The proposed integrated method mainly contains two parallel features analysis modules: first, temporal multiscale features structures of the nonlinear and nonstationary turbulent cascade are identified by Variational Mode Decomposition (VMD); then, the ocean microstructure shear fluctuation data are decomposed into a series of intrinsic mode functions (IMFs), which are characterized by different time scales and frequency bandwidths. The local features of energy transfer are identified when the local intermittency peaks overlap and the phase-synchronization case occurs between two neighboring scales; second, the spatial statistical characteristics of the turbulent energy dissipation are quantitatively studied. The cumulative probability distribution functions (CPDFs) of kinetic energy dissipation are approximated well by a normal distribution, indicating that the turbulent dissipation process exhibits a robust spatial scaling correlation and a few intense dissipation locations dominate the integrated process. Finally, the proposed integrated method is evaluated through experiments using an autonomous vertical reciprocating profiler deployed in the South China Sea. Preliminary experimental results show that the proposed novel method is useful to improve our understanding of turbulent energy transfer and the evolution process in the ocean dynamic systems. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 2349 KiB

Open AccessArticle

Vibration and Flutter of a Honeycomb Sandwich Plate with Zero Poisson’s Ratio

by Junhua Zhang, Zhaochen Yan and Lili Xia

Mathematics 2021, 9(19), 2528; https://doi.org/10.3390/math9192528 - 8 Oct 2021

Cited by 18 | Viewed by 3075

Abstract

A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed [...] Read more.

A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed for free vibrations and flutter under supersonic airflows. The equivalent elastic parametric formulas of the honeycomb core for zero Poisson’s ratio are proposed. The models are compared for their natural frequencies by theoretical and finite element methods respectively, which verifies the validity of the equivalent elastic parametric formulas and the model for the honeycomb sandwich plate with zero Poisson’s ratio. The influence of the geometric parameters of the honeycomb plate on the vibration frequencies is obtained. Three kinds of honeycomb cores, namely, regular hexagon, auxetic and hybrid with zero Poisson’s ratio, are compared through natural frequencies of the sandwich plate. It is found that the frequency of the zero Poisson’s ratio honeycomb sandwich plate is the second one when the other parameters are the same. The flutter of the honeycomb plate is analyzed by using the first order piston theory under supersonic flows. The critical flutter velocity of the plate is obtained, and the influence of geometric parameters of the honeycomb plate on the critical flutter velocities is obtained. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 3311 KiB

Open AccessArticle

Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

by Yury Shestopalov and Azizaga Shakhverdiev

Symmetry 2021, 13(10), 1884; https://doi.org/10.3390/sym13101884 - 6 Oct 2021

Cited by 13 | Viewed by 1886

Abstract

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes [...] Read more.

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

28 pages, 72229 KiB

Open AccessArticle

A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports

by Yeqing Jin, Ruiping Yang, Hengxu Liu, Haiwei Xu and Hailong Chen

Appl. Sci. 2021, 11(19), 9141; https://doi.org/10.3390/app11199141 - 1 Oct 2021

Cited by 5 | Viewed by 2426

Abstract

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed [...] Read more.

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 330 KiB

Open AccessArticle

Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

by Ruofeng Rao, Jialin Huang and Xinsong Yang

Mathematics 2021, 9(19), 2446; https://doi.org/10.3390/math9192446 - 1 Oct 2021

Cited by 1 | Viewed by 1747

Abstract

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the [...] Read more.

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 3372 KiB

Open AccessArticle

AMT Starting Control as a Soft Starter for Belt Conveyors Using a Data-Driven Method

by Yunxia Li, Lei Li and Chengliang Zhang

Symmetry 2021, 13(10), 1808; https://doi.org/10.3390/sym13101808 - 28 Sep 2021

Cited by 3 | Viewed by 2272

Abstract

Automated mechanical transmission (AMT) is used as a soft starter in this paper. To improve the soft starting quality, a novel data-driven method is studied. By analyzing and comparing five common soft-starting acceleration curves, a segmented acceleration curve is put forward to be [...] Read more.

Automated mechanical transmission (AMT) is used as a soft starter in this paper. To improve the soft starting quality, a novel data-driven method is studied. By analyzing and comparing five common soft-starting acceleration curves, a segmented acceleration curve is put forward to be used as the soft-starting acceleration curve for the AMT. Based on the prototype model free adaptive control (MFAC) method, a modified MFAC method with jerk compensation is given to control the AMT output shaft’s angular acceleration and reduce driveline shock. Compared with the methods of prototype MFAC and traditional proportion integration differentiation (PID), the modified MFAC method with jerk compensation can better control the AMT output shaft’s angular acceleration and has excellent characteristics in terms of small tracking error and smaller shock. The research results provide a novel data-driven method for AMT as a soft starter. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 4739 KiB

Open AccessArticle

An Experimental and Numerical Study on Reduction of Generated Axial Force

by Seong Han Kim, Do Hoon Kim and Gwang Hee Jo

Appl. Sci. 2021, 11(19), 8836; https://doi.org/10.3390/app11198836 - 23 Sep 2021

Cited by 1 | Viewed by 3723

Abstract

This paper proposes an experimental and numerical study to reduce the generated axial force (GAF) in a tripod constant velocity joint (CVJ). Based on the GAF model developed through kinematic and frictional analysis on the tripod CVJ, the key parameters that have a [...] Read more.

This paper proposes an experimental and numerical study to reduce the generated axial force (GAF) in a tripod constant velocity joint (CVJ). Based on the GAF model developed through kinematic and frictional analysis on the tripod CVJ, the key parameters that have a significant influence on the GAF are obtained. These parameters vary with the design parameters of the CVJ and the optimal design parameter with the lowest GAF are presented. The GAF of a tripod CVJ is estimated by the developed model, with respect to various design parameters, and the results shows that track curvature highly affects the GAF whereas contact angle hardly affects the GAF. The GAF decreases with the decrease of track curvature, and the minimum GAF occurs at −20% track curvature and +20% contact angle. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

8 pages, 304 KiB

Open AccessArticle

On the Solutions of the b-Family of Novikov Equation

by Tingting Wang, Xuanxuan Han and Yibin Lu

Symmetry 2021, 13(10), 1765; https://doi.org/10.3390/sym13101765 - 22 Sep 2021

Cited by 1 | Viewed by 1699

Abstract

In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In [...] Read more.

In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In particular, the single peakon, two-peakon, stationary kink, anti-kink, two-kink, two-anti-kink, bell-shape soliton and hat-shape soliton solutions are presented in an explicit formula. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 8614 KiB

Open AccessArticle

Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems

by Klaus Paschek, Arthur Roßmann, Michael Hausmann and Georg Hildenbrand

Appl. Sci. 2021, 11(18), 8624; https://doi.org/10.3390/app11188624 - 16 Sep 2021

Viewed by 2733

Abstract

Volcanism powered by tidal forces inside celestial bodies can provide enough energy to keep important solvents for living systems in the liquid phase. A prerequisite to calculate such tidal interactions and consequences is depending on simulations for tidal accelerations in a multi-body system. [...] Read more.

Volcanism powered by tidal forces inside celestial bodies can provide enough energy to keep important solvents for living systems in the liquid phase. A prerequisite to calculate such tidal interactions and consequences is depending on simulations for tidal accelerations in a multi-body system. Unfortunately, from measurements in many extrasolar planetary systems, only few physical and orbital parameters are well-known enough for investigated celestial bodies. For calculating tidal acceleration vectors under missing most orbital parameter exactly, a simulation method is developed that is only based on a few basic parameters, easily measurable even in extrasolar planetary systems. Such a method as the one presented here allows finding a relation between the tidal acceleration vectors and potential heating inside celestial objects. Using the values and results of our model approach to our solar system as a “gold standard” for feasibility allowed us to classify this heating in relation to different forms of volcanism. This “gold standard” approach gave us a classification measure for the relevance of tidal heating in other extrasolar systems with a reduced availability of exact physical parameters. We help to estimate conditions for the identification of potential candidates for further sophisticated investigations by more complex established methods such as viscoelastic multi-body theories. As a first example, we applied the procedures developed here to the extrasolar planetary system TRAPPIST-1 as an example to check our working hypothesis. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 3869 KiB

Open AccessArticle

Optical Solitons with Beta and M-Truncated Derivatives in Nonlinear Negative-Index Materials with Bohm Potential

by Muhammad Bilal Riaz, Jan Awrejcewicz and Adil Jhangeer

Materials 2021, 14(18), 5335; https://doi.org/10.3390/ma14185335 - 16 Sep 2021

Cited by 4 | Viewed by 4823

Abstract

In this article, we explore solitary wave structures in nonlinear negative-index materials with beta and M-truncated fractional derivatives with the existence of a Bohm potential. The consideration of Bohm potential produced quantum phase behavior in electromagnetic waves. The applied technique is the New [...] Read more.

In this article, we explore solitary wave structures in nonlinear negative-index materials with beta and M-truncated fractional derivatives with the existence of a Bohm potential. The consideration of Bohm potential produced quantum phase behavior in electromagnetic waves. The applied technique is the New extended algebraic method. By use of this approach, acquired solutions convey various types of new families containing dark, dark-singular, dark-bright, and singular solutions of Type 1 and 2. Moreover, the constraint conditions for the presence of the obtained solutions are a side-effect of this technique. Finally, graphical structures are depicted. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 32707 KiB

Open AccessArticle

Holding Force and Vertical Vibration of Emergency Gate in the Closing Process: Physical and Numerical Modelling

by Yanzhao Wang, Guobin Xu and Fang Liu

Appl. Sci. 2021, 11(18), 8440; https://doi.org/10.3390/app11188440 - 11 Sep 2021

Cited by 3 | Viewed by 2192

Abstract

A two-dimensional unsteady fluid–structure interaction numerical model was established, based on the physical model test, to investigate the influence of vertical vibration on the holding force of an emergency gate in the closing process. Gate motion was controlled by the user-defined function in [...] Read more.

A two-dimensional unsteady fluid–structure interaction numerical model was established, based on the physical model test, to investigate the influence of vertical vibration on the holding force of an emergency gate in the closing process. Gate motion was controlled by the user-defined function in Fluent. Attention was paid to the relationship between the vertical vibration, hydrodynamic loads and flow discharge. The experiment results show that holding force has three typical forms in the closing process and it is related to the service gate height. The numerical model can reflect the gate vertical vibration and the gate-closing displacement in the form of steps. Gate vertical vibration in the closing process is a motion-induced vibration caused by gate active falling. Moreover, the transition from full-flow to open-flow behind the emergency gate has a great influence on the gate vertical vibration. With a small gate opening, gate vertical vibration makes the flow discharge fluctuation increase. Furthermore, flow discharge has an influence on the gate body loads, which is mainly concentrated in the upstream plate and gate bottom. Finally, the lift force coefficient at the gate bottom is different from the standard and is mainly controlled by the outflow boundary condition. The simulation result is in good agreement with the experiment and the relative error meets engineering requirements, suggesting that the numerical model can successfully simulate the gate fluid–structure interaction and reproduce the characteristics of physical quantities in the closing process. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 1471 KiB

Open AccessArticle

Design of a Long-Pass Filter with Effects on Fluorescence Image Observation for Surgical Fluorescence Microscope Applications

by Jinkyu Kim, Kicheol Yoon and Kwanggi Kim

Symmetry 2021, 13(9), 1571; https://doi.org/10.3390/sym13091571 - 26 Aug 2021

Cited by 1 | Viewed by 2557

Abstract

The goal of oncological surgery is to completely remove the tumor. Tumors are often difficult to observe with the naked eye because of the presence of numerous blood vessels and the fact the colors of the tumor and blood vessels are similar. Therefore, [...] Read more.

The goal of oncological surgery is to completely remove the tumor. Tumors are often difficult to observe with the naked eye because of the presence of numerous blood vessels and the fact the colors of the tumor and blood vessels are similar. Therefore, a fluorescent contrast medium using a surgical microscope is used to observe the removal status of the tumor. To observe the tumor removal status using a fluorescent contrast agent, fluorescence is expressed in the tumor by irradiating with an external light source, and the expressed tumor can be confirmed through a surgical microscope. However, not only fluorescence-expressed tumors are observed under a surgical microscope, but images from an external light source are also mixed and observed. Therefore, since the surgical microscope is connected to a filter, the quality of the diagnostic image is not uniform, and it is difficult to achieve a clear observation. As a result, an asymmetric image quality phenomenon occurs in the diagnostic images. In this paper, a filter with high clarity that provides a symmetrical observation of diagnostic images is developed and manufactured. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 7413 KiB

Open AccessArticle

Spiral Bevel Gears Nonlinear Vibration Having Radial and Axial Misalignments Effects

by Moslem Molaie, Farhad S. Samani and Francesco Pellicano

Vibration 2021, 4(3), 666-678; https://doi.org/10.3390/vibration4030037 - 18 Aug 2021

Cited by 12 | Viewed by 4683

Abstract

In gear transmissions, vibration causes noise and malfunction. In actual applications, misalignments contribute to intensifying the destructive effect of vibrations. In this paper, the nonlinear dynamics of a spiral bevel gear pair, with small helix angle, considering different misalignments, are deeply investigated. Axial [...] Read more.

In gear transmissions, vibration causes noise and malfunction. In actual applications, misalignments contribute to intensifying the destructive effect of vibrations. In this paper, the nonlinear dynamics of a spiral bevel gear pair, with small helix angle, considering different misalignments, are deeply investigated. Axial misalignment, radial misalignment, and the combination of these two types are considered in this study. The governing equation is numerically solved through an implicit Runge–Kutta scheme. Since the main goal of this study is the analysis of the dynamic scenario, the mesh stiffness of the gear pair is obtained from the literature. The dynamical system is nonlinear and time-varying; it is analyzed through time responses, phase portraits, Poincaré maps, and bifurcation diagrams. Results show that, among the considered three cases with different types of misalignments, the spiral bevel gear with axial misalignment is the worst destructive case; aperiodic, subharmonic, and multiperiod responses are observable for this case. It is interesting that the chaotic responses for the case, having both types of misalignments, are less likely for the case with axial misalignment, only. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 10125 KiB

Open AccessArticle

In-Cylinder Oxygen Concentration Estimation Based on Virtual Measurement and Data Fusion Algorithm for Turbocharged Diesel Engines

by Qi Zhang, Bin Wen, Xuemei Zhang, Kai Wu, Xinyu Wu and Yinyou Zhang

Appl. Sci. 2021, 11(16), 7594; https://doi.org/10.3390/app11167594 - 18 Aug 2021

Cited by 1 | Viewed by 1680

Abstract

In-cylinder oxygen concentration (ICOC) is critical for advanced combustion control of internal combustion engines, and is hard to be accessed in commercial measurements. In existing research, ICOC is predicted by conventional dynamical model based on mass/energy conservation, which suffers from uncertainties such as [...] Read more.

In-cylinder oxygen concentration (ICOC) is critical for advanced combustion control of internal combustion engines, and is hard to be accessed in commercial measurements. In existing research, ICOC is predicted by conventional dynamical model based on mass/energy conservation, which suffers from uncertainties such as inaccuracy of volumetric efficiency or the error of orifice geometry. In this paper, we enhance the ICOC estimation by implementing two vital strategies. Firstly, we introduce a method called virtual measurement to resist the conventional model uncertainties, in this method we modeling the ICOC as a function of ignition delay which can be obtained by measuring the in-cylinder pressure. Secondly, we apply Kalman filter to fuse the ICOC results from the conventional dynamical model and the virtual measurement. The data fusion algorithm turns the estimation to a predictor-corrector fashion, which further improves the overall accuracy and robustness. The proposed approach is validated through a calibrated GT-Power engine model. The results show that the estimation error can be achieved form at worst 0.03 to at best 0.01 on steady state. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

26 pages, 12662 KiB

Open AccessArticle

Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

by Nasser A. Saeed, Emad Mahrous, Emad Abouel Nasr and Jan Awrejcewicz

Symmetry 2021, 13(8), 1502; https://doi.org/10.3390/sym13081502 - 16 Aug 2021

Cited by 29 | Viewed by 5235

Abstract

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control [...] Read more.

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in

+ X, + Y, - X, - Y

directions)

,

while the other four poles are inserted in a way such that each pole makes 45° with two of the axes

+ X, + Y, - X, - Y

. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in

X

and

Y

directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 2432 KiB

Open AccessArticle

Stability Analysis of Pseudo-Almost Periodic Solution for a Class of Cellular Neural Network with D Operator and Time-Varying Delays

by Weide Liu, Jianliang Huang and Qinghe Yao

Mathematics 2021, 9(16), 1951; https://doi.org/10.3390/math9161951 - 15 Aug 2021

Cited by 5 | Viewed by 2563

Abstract

Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class [...] Read more.

Cellular neural networks with D operator and time-varying delays are found to be effective in demonstrating complex dynamic behaviors. The stability analysis of the pseudo-almost periodic solution for a novel neural network of this kind is considered in this work. A generalized class neural networks model, combining cellular neural networks and the shunting inhibitory neural networks with D operator and time-varying delays is constructed. Based on the fixed-point theory and the exponential dichotomy of linear equations, the existence and uniqueness of pseudo-almost periodic solutions are investigated. Through a suitable variable transformation, the globally exponentially stable sufficient condition of the cellular neural network is examined. Compared with previous studies on the stability of periodic solutions, the global exponential stability analysis for this work avoids constructing the complex Lyapunov functional. Therefore, the stability criteria of the pseudo-almost periodic solution for cellular neural networks in this paper are more precise and less conservative. Finally, an example is presented to illustrate the feasibility and effectiveness of our obtained theoretical results. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 261 KiB

Open AccessArticle

Oscillation Criteria of Second-Order Dynamic Equations on Time Scales

by Ya-Ru Zhu, Zhong-Xuan Mao, Shi-Pu Liu and Jing-Feng Tian

Mathematics 2021, 9(16), 1867; https://doi.org/10.3390/math9161867 - 6 Aug 2021

Cited by 10 | Viewed by 1720

Abstract

In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation. [...] Read more.

In this paper, we consider the oscillation behavior of the following second-order nonlinear dynamic equation.

{(λ (s) Ψ (\frac{1}{φ^{Δ} (s)} {(y (φ (s)))}^{Δ}))}^{Δ} + η (s) Φ (y (τ (s))) = 0, s \in {[s_{0}, \infty)}_{T} .

By employing generalized Riccati transformation and inequality scaling technique, we establish some oscillation criteria. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

17 pages, 8744 KiB

Open AccessArticle

Actuator-Integrated Fault Estimation and Fault Tolerant Control for Electric Power Steering System of Forklift

by Xiangxiang Su and Benxian Xiao

Appl. Sci. 2021, 11(16), 7236; https://doi.org/10.3390/app11167236 - 5 Aug 2021

Cited by 7 | Viewed by 2457

Abstract

For the problem of actuator-integrated fault estimation (FE) and fault tolerant control (FTC) for the electric power steering (EPS) system of a forklift, firstly, a dynamic model of a forklift EPS system with actuator faults was established; then, an integrated FE and FTC [...] Read more.

For the problem of actuator-integrated fault estimation (FE) and fault tolerant control (FTC) for the electric power steering (EPS) system of a forklift, firstly, a dynamic model of a forklift EPS system with actuator faults was established; then, an integrated FE and FTC design was proposed. The nonlinear unknown input observer (NUIO) was proposed to estimate the system states and actuator faults, and an adaptive sliding mode FTC system was constructed based on it. The gain of the observer and controller is obtained by

H_{\infty}

optimization and one-step linear matrix inequality (LMI) formula operation in order to realize the overall optimal design of an FTC system. Finally, the experimental results show that when actuator failure occurs, the proposed integrated FE and FTC were more accurate than the decentralized design to estimate the system states and the actuator faults. The proposed fault-tolerant controller can more effectively restore the power assist performance of the steering power motor in case of failure and effectively ensure the safety and reliability of the forklift EPS system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 1088 KiB

Open AccessArticle

Wheel Flats in the Dynamic Behavior of Ballasted and Slab Railway Tracks

by Cecilia Vale

Appl. Sci. 2021, 11(15), 7127; https://doi.org/10.3390/app11157127 - 2 Aug 2021

Cited by 15 | Viewed by 2936

Abstract

Wheel flats induce high-impact loads with relevance for the safety of the vehicle in operation as they can contribute to broken axles, hot axle boxes, and damaged rolling bearings and wheels. The high loads also induce damage in the track components such as [...] Read more.

Wheel flats induce high-impact loads with relevance for the safety of the vehicle in operation as they can contribute to broken axles, hot axle boxes, and damaged rolling bearings and wheels. The high loads also induce damage in the track components such as rails and sleepers. Although this subject has been studied numerically and experimentally over the last few years, the wheel flat problem has focused on ballasted tracks, and there is a need to understand the phenomena also for slab tracks. In this research, a numerical approach was used to show the effects of the wheel flats with different geometric configurations on the dynamic behavior of a classical ballasted track and a continuous slab track. Several wheel flat geometries and different vehicle speeds were considered. The nonlinear Hertzian contact model was used because of the high dynamic variation of the interaction of the load between the vehicle and the rail. The results evidenced that, for the same traffic conditions, the dynamic force was higher on the slab track than on the ballasted one, contrary to the maximum vertical displacement, which was higher on the ballasted track due to the track differences regarding the stiffness and frequency response. The results are useful for railway managers who wish to monitor track deterioration under the regulatory limits. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 7044 KiB

Open AccessArticle

Dynamic Analysis of Ball Screw Feed System with the Effects of Excitation Amplitude and Design Parameters

by Chang Liu, Chunyu Zhao, Zhendong Liu and Shuai Wang

Appl. Sci. 2021, 11(15), 7070; https://doi.org/10.3390/app11157070 - 30 Jul 2021

Cited by 5 | Viewed by 9194

Abstract

In this paper, a nine degree-of-freedom dynamic model of the ball screw feed system considering the contact nonlinearity between balls and raceways is established to analyze the vibration characteristics. The position relationship between raceway centers for the ball screw and bearings is determined [...] Read more.

In this paper, a nine degree-of-freedom dynamic model of the ball screw feed system considering the contact nonlinearity between balls and raceways is established to analyze the vibration characteristics. The position relationship between raceway centers for the ball screw and bearings is determined by using the homogeneous coordinate transformation, and then the restoring force functions along the axial and lateral directions are derived. The dynamic equations of the feed system are solved by using Newmark method, and the proposed model is verified by the experimental method. Furthermore, the effect of the excitation amplitude on the axial vibration of the feed system is investigated by the frequency-amplitude curve and 3-D frequency spectrum. With the increase of excitation amplitude, the dynamic response of the feed system exits the softening, hardening type nonlinearity and jump phenomenon. Additionally, the effects of the initial contact angle, length of screw shaft and number of loaded balls on the axial vibration of the feed system in the resonance region are discussed. The results show that the dynamic model established in this paper is suitable for improving the machining accuracy and stability of the ball screw feed system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 20835 KiB

Open AccessArticle

Modelling Functional Shifts in Two-Species Hypercycles

by Bernat Bassols, Ernest Fontich, Daniel Oro, David Alonso and Josep Sardanyés

Mathematics 2021, 9(15), 1809; https://doi.org/10.3390/math9151809 - 30 Jul 2021

Cited by 2 | Viewed by 4180

Abstract

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural [...] Read more.

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural shifts due to environmental and ecological changes. Such changes could involve switches from cooperative to antagonistic interactions, in what we call a functional shift. In this article, we investigate a model for a two-member hypercycle model, considering that one species performs a functional shift. First, we introduce the model dynamics without functional shifts to illustrate the dynamics only considering obligate and facultative cooperation. Then, two more cases maintaining cross-catalysis are considered: (i) a model describing the dynamics of ribozymes where a fraction of the population of one replicator degrades the other molecular species while the other fraction still receives catalytic aid; and (ii) a system in which a given fraction of the population predates on the cooperating species while the rest of the population still receives aid. We have characterised the key bifurcation parameters determining extinction, survival, and coexistence of species. We show that predation, regardless of the fraction that benefits from it, does not significantly change dynamics with respect to the degradative case (i), thus conserving dynamics and bifurcations. Their biological significance is interpreted, and their potential implications for the dynamics of early replicators and ecological species are outlined. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 10078 KiB

Open AccessArticle

Numerical Parametric Study on the Effectiveness of the Contact-Point Response of a Stationary Vehicle for Bridge Health Monitoring

by Ibrahim Hashlamon, Ehsan Nikbakht, Ameen Topa and Ahmed Elhattab

Appl. Sci. 2021, 11(15), 7028; https://doi.org/10.3390/app11157028 - 29 Jul 2021

Cited by 7 | Viewed by 2960

Abstract

Indirect bridge health monitoring is conducted by running an instrumented vehicle over a bridge, where the vehicle serves as a source of excitation and as a signal receiver; however, it is also important to investigate the response of the instrumented vehicle while it [...] Read more.

Indirect bridge health monitoring is conducted by running an instrumented vehicle over a bridge, where the vehicle serves as a source of excitation and as a signal receiver; however, it is also important to investigate the response of the instrumented vehicle while it is in a stationary position while the bridge is excited by other source of excitation. In this paper, a numerical model of a stationary vehicle parked on a bridge excited by another moving vehicle is developed. Both stationary and moving vehicles are modeled as spring–mass single-degree-of-freedom systems. The bridges are simply supported and are modeled as 1D beam elements. It is known that the stationary vehicle response is different from the true bridge response at the same location. This paper investigates the effectiveness of contact-point response in reflecting the true response of the bridge. The stationary vehicle response is obtained from the numerical model, and its contact-point response is calculated by MATLAB. The contact-point response of the stationary vehicle is investigated under various conditions. These conditions include different vehicle frequencies, damped and undamped conditions, different locations of the stationary vehicle, road roughness effects, different moving vehicle speeds and masses, and a longer span for the bridge. In the time domain, the discrepancy of the stationary vehicle response with the true bridge response is clear, while the contact-point response agrees well with the true bridge response. The contact-point response could detect the first, second, and third modes of frequency clearly, unlike the stationary vehicle response spectra. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 4161 KiB

Open AccessArticle

Research on the Reliability Allocation Method of Smart Meters Based on DEA and DBN

by Juan Zhou, Zonghuan Wu and Zhonghua Yu

Appl. Sci. 2021, 11(15), 6901; https://doi.org/10.3390/app11156901 - 27 Jul 2021

Cited by 2 | Viewed by 2556

Abstract

Reliability allocation can reasonably determine the reliability index of each unit in the system to ensure product quality in design, manufacturing, testing and acceptance. In the design process of the smart meter, the preliminary reliability allocation results may be unreasonable, so in the [...] Read more.

Reliability allocation can reasonably determine the reliability index of each unit in the system to ensure product quality in design, manufacturing, testing and acceptance. In the design process of the smart meter, the preliminary reliability allocation results may be unreasonable, so in the middle and later stages of the design stage, the reliability needs to be reallocated. The traditional allocation method has some limitations, such as strong subjectivity, large amount of calculation and too much reliance on expert judgment. In order to solve these problems, this paper presents a multi-method fusion method of reliability allocation. First, this paper uses the goal-oriented methodology (GO methodology) to integrate dynamic Bayesian networks (DBNs) to predict the reliability of smart meters. Second, a data envelopment analysis (DEA) reliability allocation model is established, the posterior probability obtained by DBN reasoning together with the failure rate and structural complexity of each unit are used as the output indicators of this model. Finally, the reliability allocation weight is calculated by using the efficiency value obtained from the DEA reliability allocation model. The validity and accuracy of this method is verified by an accelerated life test. This provides a new idea for reliability reallocation of smart meters. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 2543 KiB

Open AccessArticle

Maximum Admissible Slip of Tractor Wheels without Disturbing the Soil Structure

by Volodymyr Bulgakov, Aivars Aboltins, Hristo Beloev, Volodymyr Nadykto, Volodymyr Kyurchev, Valerii Adamchuk and Viktor Kaminskiy

Appl. Sci. 2021, 11(15), 6893; https://doi.org/10.3390/app11156893 - 27 Jul 2021

Cited by 7 | Viewed by 2659

Abstract

One of the most important parameters that characterize the traction-coupling properties of a wheeled tractor is its slip. The more tractor’s gross traction exists, the higher its traction-coupling properties are. However, this gross traction should not exceed its maximum possible value, which, in [...] Read more.

One of the most important parameters that characterize the traction-coupling properties of a wheeled tractor is its slip. The more tractor’s gross traction exists, the higher its traction-coupling properties are. However, this gross traction should not exceed its maximum possible value, which, in turn out, is to be determined by the maximum permissible slip,

δ_{m a x}

. This article provides the equation to calculate this crucial parameter and establishes the dependencies between the tractor’s slip and soil structure coefficient. It was shown that the value of

δ_{m a x}

basically depends on such soil characteristics as the bulk deformation coefficient and the coefficient of rolling resistance. Calculations showed that, for the average value of the soil bulk deformation coefficient at

4000 kN \cdot m^{- 3}

, the average value of rolling resistance coefficient at 0.16, and the ratio value of the maximum permissible soil pressure to the tractor wheel rolling radius at

222 kPa \cdot m^{- 1}

, the maximum permitted amount slip of the tractor wheels should not exceed 15%. With more slip, the soil structure deteriorates significantly. In this case, its structure coefficient may be less than critical, equal to 0.4. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 401 KiB

Open AccessArticle

Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems

by Yiqing Xue and Ping Zhao

Mathematics 2021, 9(14), 1663; https://doi.org/10.3390/math9141663 - 15 Jul 2021

Cited by 6 | Viewed by 2637

Abstract

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear [...] Read more.

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 5378 KiB

Open AccessArticle

Sliding Mode-Based Slip Control of Compact Electric Vehicle Truck for Varying Load and Yaw Rate

by Hyeon-Woo Kim and Hyun-Rok Cha

Appl. Sci. 2021, 11(14), 6465; https://doi.org/10.3390/app11146465 - 13 Jul 2021

Cited by 3 | Viewed by 2334

Abstract

Vehicle stability is a critical problem, especially for compact electric vehicle (EV) trucks, owing to the impact of the cargo weight and cornering characteristics. In this study, this problem was approached by mathematically formulating the change in the understeer characteristics of an EV [...] Read more.

Vehicle stability is a critical problem, especially for compact electric vehicle (EV) trucks, owing to the impact of the cargo weight and cornering characteristics. In this study, this problem was approached by mathematically formulating the change in the understeer characteristics of an EV truck as variable mass understeer gradient (VMUG) according to the vehicle cargo weight to design the reference yaw rate without the need to consider cornering stiffness. Comparison was made with the conventional methods by applying the VMUG-based slip control while simulating the yaw rate and side-slip tracking performance of the compact EV model for normal loading and overloading conditions. The simulation results demonstrate the superior performance of the proposed method compared to the existing methods. The proposed method has the potential for application for stability enhancement in non-electric and general-purpose vehicles as well. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 6723 KiB

Open AccessArticle

Energy Consumption Evaluation of Active Tillage Machines Using Dynamic Modelling

by Zoltán Forgó, Ferenc Tolvaly-Roșca, Judit Pásztor and Attila Kovari

Appl. Sci. 2021, 11(14), 6240; https://doi.org/10.3390/app11146240 - 6 Jul 2021

Cited by 7 | Viewed by 2708

Abstract

Soil tillage is a very energy-intensive operation. A general expectation is to reduce energy consumption and reduce soil compaction with as few turns and interventions as possible. Thus, more and more attention is being paid to the use of active tillage machines. The [...] Read more.

Soil tillage is a very energy-intensive operation. A general expectation is to reduce energy consumption and reduce soil compaction with as few turns and interventions as possible. Thus, more and more attention is being paid to the use of active tillage machines. The aim of the present work is to test a new approach to optimize PTO-driven tilling machine operations regarding energy consumption. A real, active tillage machine, the MSS-140 type spading machine, was investigated in the Matlab^® Simscape™ environment. The solid model of the spading machine was built using actual dimensions. The work done by a single spade is broken down into elementary processes. The acting forces on the implement, in each elementary process for different advancing speeds, were modelled and calculated. The model is suitable for illustrating the dynamics of loads and for calculating the mechanical work. The model was also tested in comparison with real fuel consumption. The consumed fuel quantity was measured and the energy requirement for the model calculated at three advancing speeds. A comparison between the measured and calculated energy consumption values was made: the calculated results are similar to the measured values; the mean difference is 9.91%, with a standard deviation 3.3%. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 3476 KiB

Open AccessArticle

Continuous Control Set Predictive Current Control for Induction Machine

by Toni Varga, Tin Benšić, Vedrana Jerković Štil and Marinko Barukčić

Appl. Sci. 2021, 11(13), 6230; https://doi.org/10.3390/app11136230 - 5 Jul 2021

Cited by 5 | Viewed by 2422

Abstract

A speed tracking control method for induction machine is shown in this paper. The method consists of outer speed control loop and inner current control loop. Model predictive current control method without the need for calculation of the weighing factors is utilized for [...] Read more.

A speed tracking control method for induction machine is shown in this paper. The method consists of outer speed control loop and inner current control loop. Model predictive current control method without the need for calculation of the weighing factors is utilized for the inner control loop, which generates a continuous set of voltage reference values that can be modulated and applied by the inverter to the induction machine. Interesting parallels are drawn between the developed method and state feedback principles that helped with the analysis of the stability and controllability. Simple speed and rotor flux estimator is implemented that helps achieve sensorless control. Simulation is conducted and the method shows great performance for speed tracking in a steady state, and during transients as well. Additionally, compared to the finite control set predictive current control, it shows less harmonic content in the generated torque on the rotor shaft. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

33 pages, 1508 KiB

Open AccessReview

Dead-Time Compensation for the First-Order Dead-Time Processes: Towards a Broader Overview

by Mikulas Huba, Pavol Bistak, Damir Vrancic and Katarina Zakova

Mathematics 2021, 9(13), 1519; https://doi.org/10.3390/math9131519 - 29 Jun 2021

Cited by 12 | Viewed by 4736

Abstract

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control [...] Read more.

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 403 KiB

Open AccessArticle

On Some Reversible Cubic Systems

by Barbara Arcet and Valery G. Romanovski

Mathematics 2021, 9(12), 1446; https://doi.org/10.3390/math9121446 - 21 Jun 2021

Cited by 3 | Viewed by 1868

Abstract

We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components [...] Read more.

We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems Mathematica and Singular. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

17 pages, 28695 KiB

Open AccessArticle

Helmholtz Resonance Frequency of the Synthetic Jet Actuator

by Paweł Gil, Joanna Wilk and Michał Korzeniowski

Appl. Sci. 2021, 11(12), 5666; https://doi.org/10.3390/app11125666 - 18 Jun 2021

Cited by 12 | Viewed by 2823

Abstract

This paper presents the results of experimental investigations of 108 geometrical configurations of a loudspeaker-driven synthetic jet (SJ) actuator. The considered cases of the SJ actuator were characterized by a high coupling ratio. The experiment was performed to determine the impact of geometry [...] Read more.

This paper presents the results of experimental investigations of 108 geometrical configurations of a loudspeaker-driven synthetic jet (SJ) actuator. The considered cases of the SJ actuator were characterized by a high coupling ratio. The experiment was performed to determine the impact of geometry on the Helmholtz resonance frequency. Geometrical parameters of the orifice diameter, orifice length, and cavity volume were changed within a wide range. The dependences of electrical and flow parameters that characterized the synthetic jet actuators as a function of the excitation frequency were also identified. The main goal of the research was to identify the optimal mathematical formula of the model to calculate the Helmholtz resonance frequency in the case of synthetic jet actuators. To determine the model that was characterized by the best fit of the experimental results, an additional geometrical dimensionless parameter, representing the ratio of the orifice cross-section area to the cross-section area of the cavity, was introduced. A significant impact of this parameter on the effective orifice length was noted. Based on the research findings, a model was obtained for which the results of the experiment were in the error range of ±6% for 95% of the measurement data. The obtained model is an improved version of the classical model used in the description of the resonance frequency in the case of a synthetic jet actuator. The model enables highly accurate determination of the Helmholtz resonance frequency at which the maximum synthetic jet actuator parameters occur. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 3667 KiB

Open AccessArticle

Zero Average Dynamic Controller for Speed Control of DC Motor

by Fredy E. Hoyos, John E. Candelo-Becerra and Alejandro Rincón

Appl. Sci. 2021, 11(12), 5608; https://doi.org/10.3390/app11125608 - 17 Jun 2021

Cited by 13 | Viewed by 2829

Abstract

This paper presents the use of the buck converter with Zero Average Dynamics to control the speed of a permanent magnet direct current motor. For this objective, we consider a fourth-order nonlinear model that describes the system’s dynamics and tests different scenarios to [...] Read more.

This paper presents the use of the buck converter with Zero Average Dynamics to control the speed of a permanent magnet direct current motor. For this objective, we consider a fourth-order nonlinear model that describes the system’s dynamics and tests different scenarios to determine how the direct current motor responds. The results show a robust speed tracking performance of the direct current motor under the reference signal and controller parameter changes and disturbances in the load torque. A non-saturated duty cycle with fixed commutation frequency is obtained in the power supply of the DC motor, and a low steady-state value of the speed tracking error is achieved in both experimental and simulation results. In summary, the effectiveness of the Zero Average Dynamics control strategy for high order systems was experimentally proved. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 2704 KiB

Open AccessArticle

Shift Strategy Optimization for Automatic Transmission of Heavy Trucks Based on Dynamic Programming Algorithm

by Heng Zhang, Xinxin Zhao, Jue Yang and Weiwei Yang

Appl. Sci. 2021, 11(12), 5555; https://doi.org/10.3390/app11125555 - 16 Jun 2021

Cited by 13 | Viewed by 4161

Abstract

The shift strategy of automatic transmission plays a vital role in the smoothness and economy of heavy-duty mining trucks. In this paper, an engine fuel consumption model, a 6 + 2 speed automatic transmission model, and a vehicle resistance model are built in [...] Read more.

The shift strategy of automatic transmission plays a vital role in the smoothness and economy of heavy-duty mining trucks. In this paper, an engine fuel consumption model, a 6 + 2 speed automatic transmission model, and a vehicle resistance model are built in MATLAB. Combined with the development of smart mining technology, the traditional two-parameter economic shift strategy is corrected based on vehicle load and road slope. The dynamic programming optimization algorithm is used to extract the best economical shift strategy under known working conditions to reduce the fuel consumption and the number of shifts. Finally, simulation experiments of the optimized shift strategy by dynamic programming in a typical mine work cycle are carried out. The simulation results show that the engine speed and output torque are maintained in a relatively stable and efficient working range by using the proposed shift strategy. Compared with the traditional two-parameter shift strategy, dynamic programming has advantages in reducing fuel consumption and shift numbers. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 28182 KiB

Open AccessArticle

Spatial Algorithms for Geometric Contact Detection in Multibody System Dynamics

by Eduardo Corral, Raúl Gismeros Moreno, Jesús Meneses, María Jesús Gómez García and Cristina Castejón

Mathematics 2021, 9(12), 1359; https://doi.org/10.3390/math9121359 - 11 Jun 2021

Cited by 18 | Viewed by 3726

Abstract

In the present work, different algorithms for contact detection in multibody systems based on smooth contact modelling approaches are presented. Beginning with the simplest ones, some difficult interactions are subsequently introduced. In addition, a brief overview on the different kinds of contact/impact modelling [...] Read more.

In the present work, different algorithms for contact detection in multibody systems based on smooth contact modelling approaches are presented. Beginning with the simplest ones, some difficult interactions are subsequently introduced. In addition, a brief overview on the different kinds of contact/impact modelling is provided and an underlining of the advantages and the drawbacks of each of them is determined. Finally, some practical examples of each interaction are presented and analyzed and an outline of the issues arisen during the design process and how they have been solved in order to obtain stable and accurate results is given. The main goal of this paper is to provide a resource for the early-stage researchers in the field that serves as an introduction to the modelling of simple contact/impact events in the context of multibody system dynamics. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

23 pages, 1901 KiB

Open AccessArticle

Numerical Study of the Influence of the Inlet Turbulence Length Scale on the Turbulent Boundary Layer

by Young-Tae Lee, Lokesh Kalyan Gutti and Hee-Chang Lim

Appl. Sci. 2021, 11(11), 5177; https://doi.org/10.3390/app11115177 - 2 Jun 2021

Cited by 3 | Viewed by 3475

Abstract

In the past half century, large eddy simulations (LESs) have played an important role in turbulent flow simulation and improving the performance of computing technology. To generate a fully developed turbulent boundary layer in the channel domain using LES, suitable inflow conditions along [...] Read more.

In the past half century, large eddy simulations (LESs) have played an important role in turbulent flow simulation and improving the performance of computing technology. To generate a fully developed turbulent boundary layer in the channel domain using LES, suitable inflow conditions along with turbulent characteristics are required. This study aimed to clarify the effect of the integral length scale on the generation of turbulent boundary layers. To accomplish this, an artificially created boundary layer was imposed on the inlet section, which gradually evolved into a fully developed turbulent boundary layer flow inside the numerical domain. In this study, the synthetic inflow method, which is a commonly employed technique, was used by imposing the spatial and temporal correlation between two different points on the inlet section. In addition, we conducted parametric length scale studies on the inlet section and compared our results with existing data. The results showed that the larger length scales in the spanwise direction were not only effective in achieving the target shape of a fully developed turbulent boundary layer, but also developed it faster than the smaller length scales. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 1533 KiB

Open AccessReview

Determination of Mesh Stiffness of Gear—Analytical Approach vs. FEM Analysis

by Jan Flek, Martin Dub, Josef Kolář, František Lopot and Karel Petr

Appl. Sci. 2021, 11(11), 4960; https://doi.org/10.3390/app11114960 - 28 May 2021

Cited by 20 | Viewed by 5632

Abstract

This paper focuses on modeling the time-varying stiffness of spur gearings, which in dynamic models of transmission systems acts as an important element of the internal excitation of the dynamic system. Here are introduced ways to approach the modeling of gear stiffness using [...] Read more.

This paper focuses on modeling the time-varying stiffness of spur gearings, which in dynamic models of transmission systems acts as an important element of the internal excitation of the dynamic system. Here are introduced ways to approach the modeling of gear stiffness using analytical calculations, which allow to model the course of mesh stiffness depending on its rotation. For verification of used analytical model were created five different gearings, and based on their geometry, the respective stiffness curves were analytically determined. Subsequently, a finite element simulation was performed in the Abaqus CAE software. Due to this software, it was possible to identify and objectively compare the stiffness curves and further determine the suitability of using the analytical model to determine the mesh stiffness of gearing. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

14 pages, 276 KiB

Open AccessArticle

A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

by Hari Mohan Srivastava, Sotiris K. Ntouyas, Mona Alsulami, Ahmed Alsaedi and Bashir Ahmad

Appl. Sci. 2021, 11(11), 4798; https://doi.org/10.3390/app11114798 - 24 May 2021

Cited by 7 | Viewed by 1980

Abstract

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed [...] Read more.

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

14 pages, 1212 KiB

Open AccessCommunication

Direct Calculation of the Group Velocity for Two-Dimensional Complex, Composite and Periodic Structures Using a Wave and Finite Element Scheme

by Muhammad Khalid Malik, Dimitrios Chronopoulos and Francesco Ciampa

Appl. Sci. 2021, 11(10), 4319; https://doi.org/10.3390/app11104319 - 11 May 2021

Cited by 4 | Viewed by 2954

Abstract

Guided waves have immense potential for structural health monitoring applications in numerous industries including aerospace. It is necessary to evaluate guided wave dispersion characteristics, i.e., group velocity and phase velocity profiles, for using them effectively. For complex structures, the profiles can have highly [...] Read more.

Guided waves have immense potential for structural health monitoring applications in numerous industries including aerospace. It is necessary to evaluate guided wave dispersion characteristics, i.e., group velocity and phase velocity profiles, for using them effectively. For complex structures, the profiles can have highly irregular shapes. In this work, a direct method for calculating the group velocity profiles for complex, composite, and periodic structures using a wave and finite element scheme is presented. The group velocity calculation technique is easy to implement, highly computationally efficient, and works with the standard finite element formulation. The major contribution is summarised in the form of a comprehensive algorithm for calculating the group velocity profiles. The method is compared with the existing analytical and numerical methods for calculation of dispersion curves. Finally, an experimental study in a multilayered composite plate is conducted and the results are found to be in good agreement. The technique is suitable to be used in all guided wave application areas such as material characterisation, non-destructive testing, and structural health monitoring. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 1977 KiB

Open AccessArticle

Mean Square Consensus of Nonlinear Multi-Agent Systems under Markovian Impulsive Attacks

by Huan Luo, Yinhe Wang, Xuexi Zhang, Peitao Gao and Haoxiang Wen

Appl. Sci. 2021, 11(9), 3926; https://doi.org/10.3390/app11093926 - 26 Apr 2021

Cited by 2 | Viewed by 2215

Abstract

This paper focuses primarily on the mean square consensus problem of a class of nonlinear multi-agent systems suffering from stochastic impulsive deception attacks. The attacks here are modeled by completely stochastic destabilizing impulses, where their gains and instants satisfy all distributions and the [...] Read more.

This paper focuses primarily on the mean square consensus problem of a class of nonlinear multi-agent systems suffering from stochastic impulsive deception attacks. The attacks here are modeled by completely stochastic destabilizing impulses, where their gains and instants satisfy all distributions and the Markovian process. Compared with existing methods, which assume that only gains are stochastic, it is difficult to deal with systems with different types of random variables. Thus, estimating the influence of these different types on the consensus problem is a key point of this paper. Based on the properties of stochastic processes, some sufficient conditions to solve the consensus problem are derived and some special cases are considered. Finally, a numerical example is given to illustrate the main results. Our results show that the consensus can be obtained if impulsive attacks do not occur too frequently, and it can promote system stability if the gains are below the defined threshold. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

Topic Menu

Topic Editors

Dynamical Systems: Theory and Applications

Topic Information

Keywords

Participating Journals

Published Papers (152 papers)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI