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Recent Advances in Nonlinear Vibration and Control

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 8233

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Special Issue Editors

Dr. Nasser A. Saeed

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Guest Editor

1. Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt
2. Mathematics Department, Faculty of Science, Galala University, Galala City 43511, Egypt
3. Department of Automation, Biomechanics, and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 90924 Lodz, Poland
Interests: nonlinear dynamical systems; nonlinear vibration control; rotor active magnetic bearing systems; rotor dynamics; chaotic systems, chaos control, and synchronization; perturbation methods; bifurcation theory; delayed differential equations

Prof. Dr. Tarek Saleh Amer

E-Mail Website
Guest Editor

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Interests: nonlinear dynamics; vibrational motion; chaotic systems; rigid bodies; bifurcation; stability of dynamical systems; perturbation techniques; optimal decelerations

Special Issue Information

Dear Colleagues,

Nonlinear vibration control is becoming increasingly important in many engineering applications such as rotating machinery, aircraft, bridges, satellites, robotics, micro-electro-mechanical systems, and mechatronics, etc. The main trend is toward making the structures lighter, more flexible, and offering higher levels of performance requirements. The actuators and sensor networks are integrated into these structures to mitigate unwanted vibrations, detect damage, and sometimes change the dynamical characteristics of the structure. These structures have become known as smart, intelligent, and sometimes adaptive structures. This Special Issue aims to present the recent theoretical, numerical, and experimental approaches to various engineering systems related to nonlinear vibrations and control.

We invite scientists and engineers from the whole world who contribute to the development of nonlinear vibrations and control to submit their appreciated work for publication in this Special Issue of the MDPI journal Applied Sciences.

Dr. Nasser A. Saeed
Prof. Dr. Tarek Saleh Amer
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

nonlinear vibrations and control in rotating machinery
nonlinear vibrations and control in rotor active magnetic bearings systems
nonlinear vibrations and control in structural, mechanical, aeronautical, and electrical systems
nonlinear vibrations and control in discontinuous dynamical systems
nonlinear vibration and control of vibro-impact, self-induced, parametric or non-ideal excited systems
nonlinear chaotic systems (analysis, control, synchronization, and circuit design)
analytical, computational, and experimental techniques applied to the nonlinear vibrations analysis and control
dynamics of rigid bodies

Published Papers (7 papers)

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Editorial

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2 pages, 173 KiB

Open AccessEditorial

Special Issue on Recent Advances in Nonlinear Vibration and Control

by Nasser A. Saeed and T. S. Amer

Appl. Sci. 2023, 13(19), 10741; https://doi.org/10.3390/app131910741 - 27 Sep 2023

Viewed by 462

Abstract

The topics of nonlinear vibration and control have garnered much interest from scientists over the last few decades due to their widespread applications in various fields, such as physics and engineering [...] Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

Research

Jump to: Editorial

18 pages, 965 KiB

Open AccessArticle

Causality Analysis with Different Probabilistic Distributions Using Transfer Entropy

by Michał J. Falkowski and Paweł D. Domański

Appl. Sci. 2023, 13(10), 5849; https://doi.org/10.3390/app13105849 - 9 May 2023

Cited by 3 | Viewed by 1014

Abstract

This paper presents the results of an analysis of causality detection in a multi-loop control system. The investigation focuses on application of the Transfer Entropy method, which is not commonly used during the exact construction of information and material flow pathways in the field of automation. Calculations are performed on simulated multi-loop control system data obtained from a system with a structure known a priori. The model incorporates the possibility of freely changing its parameters and of applying noise with different properties. In addition, a method for determining the entropy transfer between process variables is investigated. The fitting of different variants of the probability distribution functions to the data is crucial for effective evaluation of the Transfer Entropy approach. The obtained results allow for suggestions to be formulated with respect to choosing which probability function the transfer entropy should be based upon. Moreover, we provide a proposal for the design of a causality analysis approach that can reliably obtain information relationships. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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20 pages, 1574 KiB

Open AccessArticle

Controller for an Asymmetric Underactuated Hovercraft in Terms of Quasi-Velocities

by Przemyslaw Herman

Appl. Sci. 2023, 13(8), 4965; https://doi.org/10.3390/app13084965 - 14 Apr 2023

Cited by 1 | Viewed by 1063

Abstract

In this paper, a nonlinear controller for tracking a desired trajectory for an underactuated hovercraft is considered. It is a modification of a method known from the literature. However, the control algorithm considered here has two important features that differ from the mentioned control strategy. First, it concerns the case when the center of mass does not coincide with the geometric center, which results in additional forces and moments of force. The lack of symmetry causes the original trajectory tracking method not to take this fact into account, while the proposed approach is a generalization of the known concept. Here, a diagonalization of the inertia matrix has been applied, by means of a velocity transformation, which made it possible to reduce the symmetric matrix to a diagonal form. Secondly, the transformed quasi-velocity equations of motion allow some insight into the dynamics of the vehicle as it moves, which was not shown in the source work. The offered approach was verified by numerical tests for a hovercraft model with three DOF and for two desired trajectories. The method can be useful in preliminary simulation studies at the controller selection stage without experimental validation. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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15 pages, 1783 KiB

Open AccessArticle

Vibration Fatigue Life Reliability Cable Trough Assessment by Using Weibull Distribution

by Jesús M. Barraza-Contreras, Manuel R. Piña-Monarrez and Roberto C. Torres-Villaseñor

Appl. Sci. 2023, 13(7), 4403; https://doi.org/10.3390/app13074403 - 30 Mar 2023

Cited by 2 | Viewed by 956

Abstract

In this paper, the formulation to incorporate the used vibration profile, the stress generated by the product’s application, mass, and the resonance frequency is given. After that, based on the vibration output data, the two-parameter Weibull distribution is used to predict the corresponding [...] Read more.

A_{r e s}

), and by using a dynamic stress factor

(σ_{d y n})

. In addition, the Weibull parameters are determined based on the generated maximum and minimum principal vibration stress values. In the paper we show the efficiency of the fitted Weibull distribution to predict the reliability indices, by using its Weibull shape and scale parameters, it is always possible to reproduce the principal vibration stress values. Additionally, from the numerical application, we show how to use the Weibull analysis to determine the reliability index for a desired stress or desired cycle value. Finally, we also present the guidelines to apply the proposed method to any vibration fatigue analysis where the

A_{r e s}

(used to determine the

σ_{1}

and

σ_{2}

values), and the

σ_{d y n}

value are both known. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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19 pages, 5684 KiB

Open AccessArticle

Parameter Optimization for an Accurate Swept-Sine Identification Procedure of Nonlinear Systems

by Pietro Burrascano

Appl. Sci. 2023, 13(2), 1223; https://doi.org/10.3390/app13021223 - 16 Jan 2023

Cited by 3 | Viewed by 1482

Abstract

Modeling the nonlinearity of a system is of primary importance both for optimizing its design and for controlling the behavior of physical systems operating with a wide dynamic range of input values, for which the linearity hypothesis may not be sufficient. To become of practical use, the identification of nonlinear models must be accurate and computationally efficient. For these reasons, in recent years, among the numerous models of nonlinear systems that have been proposed in the technical literature, the Hammerstein model has been widely applied as a consequence of the proposal of a new pattern identification technique based on pulse compression, which makes the identification of the model very accurate in numerous applications for which it has been adopted. Hammerstein model identification of a nonlinear system requires characterization of the linear filters present on the different branches of the model. These linear filters, which constitute the parameters of the model to be identified, must be considered with respect to their trends over time or, equivalently, in their frequency trends, as amplitude and phase responses. The identification can be considered accurate if the trends obtained for each filter adequately characterize it for the entire frequency range to which that specific filter is subjected in the normal operation of the system to be identified. This work focuses on this aspect, i.e., on the adequacy of the frequency range for which the filter is identified and on how to obtain correct identification in the entire frequency range of interest. The identification procedure based on exponential swept-sine signals defines these filters in the time domain by making use of intermediate functions that are related to the impulse responses of the model filters through a linear transformation. In this paper, we analyze, in detail, the roles of the bandwidths of both the excitation signal and the matched filter, which are the basis of the procedure, we verify the assumptions made about the amplitudes of their frequency bands, and we propose criteria for defining the bandwidths in order to maximize accuracy in model identification. The experiment performed makes it possible to verify that the proposed procedure avoids possible limitations and significantly improves the quality of the identification results, both if the description is made in the time domain and in the frequency domain. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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18 pages, 3148 KiB

Open AccessArticle

Some Dynamic Aspects of a Sextic Galactic Potential in a Rotating Reference Frame

by Munirah Alfadhli, Adel Elmandouh and Muneerah Al Nuwairan

Appl. Sci. 2023, 13(2), 1123; https://doi.org/10.3390/app13021123 - 14 Jan 2023

Cited by 2 | Viewed by 1057

Abstract

This work aims to explore some dynamic aspects of the problem of star motion that is impacted by the rotation of the galaxy, which we model as a bisymmetric potential based on a two-dimensional harmonic oscillator with sextic perturbations. We demonstrate analytically that the motion is non-integrable when certain conditions are met. The analytical results for the non-integrability are confirmed by showing the irregularity of the behavior of the motion through utilizing the Poincaré surface of a section as a numerical method. The motion equilibrium positions are detected, and their stability is discussed. We show that the force generated by the rotating frame acts as a stabilizer for the maximum equilibrium points. We display graphically that the size of the stability regions relies on the angular velocity magnitude for the frame. Through the application of Lyapunov’s theorem, periodic solutions can be constructed which are close to the equilibrium positions. Furthermore, we demonstrate that there are one or two families of periodic solutions relying on whether the equilibrium point is a saddle or stable, respectively. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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16 pages, 2149 KiB

Open AccessArticle

Performance Improvement of an NMP Mini Segway Using Sample and Hold Inputs

by Yingxu Wang and Guoming Zhu

Appl. Sci. 2023, 13(2), 1070; https://doi.org/10.3390/app13021070 - 13 Jan 2023

Cited by 1 | Viewed by 1440

Abstract

Early analytical work showed that it is possible to discretize a continuous-time non-minimum phase (NMP) system using special sample and hold inputs (SHIs) and obtain a discrete-time minimum phase (MP) system with a higher sampling rate than that of conventional zero-order sample and hold. As a result, high-gain discrete-time control law can be used to further improve closed-loop system performance since the resulting discrete-time system is MP. In this paper, this technique is adopted for performance improvement on a mini-Segway (MS), a developed robot equipped with an extremely low-cost microcontroller (Arduino). A dual-loop control tuning method was developed to optimize the overall closed-loop system performance. The system performance improvement is demonstrated by the reduction of the mini-Segway oscillation magnitude under idle conditions. The experimental results show that the low-cost microcontroller can be used for the dual-loop SHI control scheme, and the MS cart displacement oscillation magnitude is significantly reduced by more than 65% over the baseline controller. The main contribution of this paper is implementing the proposed sample and hold input (SHI) scheme into an extremely low-cost micro-controller (Arduino) and demonstrating that low-cost microcontrollers can effectively utilize the proposed SHI. Full article

(This article belongs to the Special Issue Recent Advances in Nonlinear Vibration and Control)

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