Search Results (272)

This paper investigates the stability and Hopf bifurcation problems of fractional-order quaternion-valued neural networks (FOQVNNs) with leakage delay and communication delay. Utilizing the Hamilton rule of quaternions, the fractional-order quaternion-valued time-delay neural network model is transformed into an equivalent fractional-order real-valued time-delay neural network system. Then, employing the stability theory and bifurcation theory of fractional-order dynamical systems, novel sufficient criteria are derived to ensure system stability and to induce Hopf bifurcation, respectively, using the leakage delay and the communication delay as bifurcation parameters. Furthermore, the influences of both delay types on the bifurcation behavior of FOQVNNs are analyzed in depth. To verify the correctness of the theoretical results, bifurcation diagrams and simulation results generated using MATLAB are presented. The theoretical results established in this paper provide a significant theoretical basis for the analysis and design of FOQVNNs. Full article

Elastic solutions of a differential system of vibrational responses of a bidirectional porous functionally graded plate (BPFG) are described by employing high-order normal and shear deformation theory, in the present study. Natural frequency values are computed for the plates with simply supported boundary conditions and taking into consideration the thickness stretching effect. Grading of the effective material property for the BPFG plate is defined according to a power-law distribution. Navier’s approach is applied to determine the governing differential equations solution of the studied model derived by Hamilton’s principle. To confirm the reliability of the solution and the model accuracy, a comparison study with various studies that are presented in the literature is carried out. Numerical illustrations are presented to discuss the influences of the plate geometry, the porosity, the volume fraction distribution, and the nonlocality on the vibration behaviors of the model. The dynamic responses of unidirectional and bidirectional porous functionally graded nanoplates are analyzed in detail, employing two parametric numerical examples. Numerical results show the sensitivity of frequencies to the studied parametric factors and their dependence on porosity and nonlocality coefficients. Frequencies of BPFG with uneven/even distribution porosity decrease when increasing the transverse and axial power-law indexes ($P\ne 0$), and the same effect appears when increasing the nonlocal parameter. Full article

The origin of chemical ordering in liquid and supercooled liquid Ge₂Sb₂Te₅ (GST) was investigated using ab initio molecular dynamics (AIMD) simulations. Bond dynamics were analyzed via continuous (${\mathrm{\tau }}_{\mathrm{con}}$) and intermittent (${\tau }_{int}$) lifetimes. The intermittent lifetime (${\tau }_{int}$) reveals that chemically ordered Ge-Te and Sb-Te bonds are the most stable, although ${\mathrm{\tau }}_{\mathrm{con}}$ exhibits a stability anomaly. The faster increase of ${\tau }_{int}$ for these bonds upon cooling explains the overall chemical ordering. A novel ordering mechanism was identified through the analysis of bond separation dynamics. Te-Te ‘wrong’ bonds exhibit a unique dynamic instability, breaking and separating much faster than any other bond type, which actively drives the system towards chemical order. A correlation between lifetime and bond strength, as calculated by the Integrated Crystal Orbital Hamilton Population (ICOHP), supports these dynamic findings. Chemical ordering shows a positive correlation with medium-range structural order, evidenced by the instability of 4-fold rings containing wrong bonds. This study provides a detailed dynamic origin for ordering in liquid GST, highlighting the role of Te-Te bond relaxation. Full article

This article focuses on the study of elastic beams with fractional-order inertial damping structures at both ends, with the aim of exploring their dynamic characteristics, damping effects, and parameter selection rules in depth, providing theoretical and practical support for engineering applications. Firstly, using the generalized Hamilton principle, two dynamic models of an elastic beam are established for two different boundary conditions. Next, using the complex modal analysis method, a design method for the critical damping of the first and second modes of an elastic beam was proposed for the first time, and the accuracy of the critical damping calculation formula was verified. Simulation analysis shows that the higher the derivative order and inertance, the lower the main resonance frequency, and the greater the critical damping. Then, using the main resonance amplitude and frequency attenuation rate (R_A and R_Ω) as indicators, an analysis was conducted on the impact of damper parameters on vibration suppression effects. The results indicate that the introduction of fractional-order inerter can reduce the main resonance amplitude and frequency, and critical damping plays a significant role in the vibration suppression process. Based on the optimal average R_A range (95–98%) and higher cost-effectiveness, selecting a damping value of 0.05~0.6 times the critical damping ensures better overall vibration suppression performance, providing an important reference for the vibration suppression design of elastic beams in practical engineering. Full article

With the increasing deployment of Unmanned Aerial Vehicle (UAV) swarms in uncertain and dynamically changing environments, optimal cooperative control has become essential for ensuring robust and efficient system coordination. To this end, this paper designs a data-driven optimal bipartite containment tracking control scheme for multi-UAV systems under compound uncertainties. A novel Dynamic Iteration Regulation Strategy (DIRS) is proposed, which enables real-time adjustment of the learning iteration step according to the task-specific demands. Compared with conventional fixed-step data-driven algorithms, the DIRS provides greater flexibility and computational efficiency, allowing for better trade-offs between the performance and cost. First, the optimal bipartite containment tracking control problem is formulated, and the associated coupled Hamilton–Jacobi–Bellman (HJB) equations are established. Then, a data-driven iterative policy learning algorithm equipped with the DIRS is developed to solve the optimal control law online. The stability and convergence of the proposed control scheme are rigorously analyzed. Furthermore, the control law is approximated via the neural network framework without requiring full knowledge of the model. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed DIRS-based optimal containment tracking scheme for multi-UAV systems, which can reduce the number of iterations by 88.27% compared to that for the conventional algorithm. Full article

In this work, an adaptive dynamic programming (ADP)-based event-triggered infinite-horizon ($H_{\infty }$) control algorithm is proposed for high-precision speed regulation of permanent magnet synchronous motors (PMSMs). The $H_{\infty }$ control problem of PMSM can be formulated as a two-player zero-sum differential game, and only a single critic neural network is needed to approximate the solution of the Hamilton–Jacobi–Isaacs (HJI) equations online, which significantly simplifies the control structure. Dynamically balancing control accuracy and update frequency through adaptive event-triggering mechanism significantly reduces the computational burden. Through theoretical analysis, the system state and critic weight estimation error are rigorously proved to be uniform ultimate boundedness, and the Zeno behavior is theoretically precluded. The simulation results verify the high accuracy tracking capability and the strong robustness of the algorithm under both load disturbance and shock load, and the event-triggering mechanism significantly reduces the computational resource consumption. Full article

This work analyzes the aero-elastic oscillations of cantilever beams reinforced by carbon nanotubes (CNTs). Four different distributions of single-walled CNTs are assumed as the reinforcing phase, in the thickness direction of the polymeric matrix. A modified third-order piston theory is used as an accurate tool to model the supersonic air flow, rather than a first-order piston theory. The nonlinear dynamic equation governing the problem accounts for Von Kármán-type nonlinearities, and it is derived from Hamilton’s principle. Then, the Galerkin decomposition technique is adopted to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation. This is solved analytically according to a multiple time scale method. A comprehensive parametric analysis was conducted to assess the influence of CNT volume fraction, beam slenderness, Mach number, and thickness ratio on the fundamental frequency and lateral dynamic deflection. Results indicate that FG-X reinforcement yields the highest frequency response and lateral deflection, followed by UD and FG-A patterns, whereas FG-O consistently exhibits the lowest performance metrics. An increase in CNT volume fraction and a reduction in slenderness ratio enhance the system’s stiffness and frequency response up to a critical threshold, beyond which a damped beating phenomenon emerges. Moreover, higher Mach numbers and greater thickness ratios significantly amplify both frequency response and lateral deflections, although damping rates tend to decrease. These findings provide valuable insights into the optimization of CNTR composite structures for advanced aeroelastic applications under supersonic conditions, as useful for many engineering applications. Full article

This research explores the application of NiTiNOL-steel (NiTi–ST) wire ropes as nonlinear damping devices for mitigating vibrations in composite stiffened panels. A dynamic model is formulated by coupling the composite panel with a modified Bouc–Wen hysteresis representation and employing the first-order shear deformation theory (FSDT), based on Hamilton’s principle. Using the Galerkin truncation method (GTM), the model is converted into a system of nonlinear ordinary differential equations. The dynamic response to axial harmonic excitations is analyzed, emphasizing the vibration reduction provided by the embedded NiTi–ST ropes. Finite element analysis (FEA) validates the model by comparing natural frequencies and force responses with and without ropes. A newly developed experimental apparatus demonstrates that NiTi–ST cables provide outstanding vibration damping while barely affecting the system’s inherent frequency. The N3a configuration of NiTi–ST ropes demonstrates optimal vibration reduction, influenced by excitation frequency, amplitude, length-to-width ratio, and composite layering. Full article

A rotating imperfect ring resonator of the gyroscope is modeled by a rotating thin ring with evenly distributed point masses. The free response of the rotating ring structure at constant speed is investigated, including the steady elastic deformation and wave response. The dynamic equations are formulated by using Hamilton’s principle in the ground-fixed coordinates. The coordinate transformation is applied to facilitate the solution of the steady deformation, and the displacements and tangential tension for the deformation are calculated by the perturbation method. Employing Galerkin’s method, the governing equation of the free vibration is casted in matrix differential operator form after the separation of the real and imaginary parts with the inextensional assumption. The natural frequencies are calculated through the eigenvalue analysis, and the numerical results are obtained. The effects of the point masses on the natural frequencies of the forward and backward traveling wave curves of different orders are discussed, especially on the measurement accuracy of gyroscopes for different cases. In the ground-fixed coordinates, the frequency splitting results in a crosspoint of the natural frequencies of the forward and backward traveling waves. The finite element method is applied to demonstrate the validity and accuracy of the model. Full article

Functionally graded materials (FGMs) have the potential to revolutionize the oil and gas transportation sector, due to their increased strengths and efficiencies as pipelines. Conventional pipelines frequently face serious problems such as extreme weather, pressure changes, corrosion, and stress-induced pipe bursts. By analyzing the mechanical and thermal performance of FGM-based pipes under various operating conditions, this study investigates the possibility of using them as a more reliable substitute. In the current study, the post-buckling and nonlinear vibration behaviors of pipes composed of FGMs transporting heavy crude oil were examined using a Timoshenko beam framework. The material properties of the FGM pipe were observed to change gradually across the thickness, following a power-law distribution, and were influenced by temperature variations. In this regard, two types of FGM pipes are considered: one with a metal-rich inner surface and ceramic-rich outer surface, and the other with a reverse configuration featuring metal on the outside and ceramic on the inside. The nonlinear governing equations (NGEs) describing the system’s nonlinear dynamic response were formulated by considering nonlinear strain terms through the von Kármán assumptions and employing Hamilton’s principle. These equations were then discretized using Galerkin’s method to facilitate the analytical investigation. The Runge–Kutta method was employed to address the nonlinear vibration problem. It is concluded that, compared with pipelines made from conventional materials, those constructed with FGMs exhibit enhanced thermal resistance and improved mechanical strength. Full article

In this paper, the problem of pitching attitude finite-horizon optimization for aircraft is posed with system uncertainties, external disturbances, and input constraints. First, a neural network (NN) and a nonlinear disturbance observer (NDO) are employed to estimate the value of system uncertainties and external disturbances. Taking input constraints into account, an auxiliary system is designed to compensate for the constrained input. Subsequently, the backstepping control containing NN and NDO is used to ensure the stability of systems and suppress the adverse effects caused by the system uncertainties and external disturbances. In order to avoid the derivation operation in the process of backstepping, a dynamic surface control (DSC) technique is utilized. Simultaneously, the estimations of the NN and NDO are applied to derive the backstepping control law. For the purpose of achieving finite-horizon optimization for pitching attitude control, an adaptive method termed adaptive dynamic programming (ADP) with a single NN-termed critic is applied to obtain the optimal control. Time-varying feature functions are applied to construct the critic NN in order to approximate the value function in the Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, a supplementary term is added to the weight update law to minimize the terminal constraint. Lyapunov stability theory is used to prove that the signals in the control system are uniformly ultimately bounded (UUB). Finally, simulation results illustrate the effectiveness of the proposed finite-horizon optimal attitude control method. Full article

This paper investigates the robust tracking control of unmanned aerial vehicles (UAVs) against external time-varying disturbances. First, by introducing a virtual position controller, we innovatively decouple the UAV dynamics into independent position and attitude error subsystems, transforming the robust tracking problem into two zero-sum differential games. This approach contrasts with conventional methods by treating disturbances as strategic “players”, enabling a systematic framework to address both external disturbances and model uncertainties. Second, we develop an integral reinforcement learning (IRL) framework that approximates the optimal solution to the Hamilton–Jacobi–Isaacs (HJI) equations without relying on precise system models. This model-free strategy overcomes the limitation of traditional robust control methods that require known disturbance bounds or accurate dynamics, offering superior adaptability to complex environments. Third, the proposed recursive Ridge regression with a forgetting factor (${\mathrm{R}}^3{\mathrm{F}}^2$ ) algorithm updates actor-critic-disturbance neural network (NN) weights in real time, ensuring both computational efficiency and convergence stability. Theoretical analyses rigorously prove the closed-loop system stability and algorithm convergence, which fills a gap in existing data-driven control studies lacking rigorous stability guarantees. Finally, numerical results validate that the method outperforms state-of-the-art model-based and model-free approaches in tracking accuracy and disturbance rejection, demonstrating its practical utility for engineering applications. Full article

This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams demonstrates that HSDT yields more accurate predictions than the Classical Beam Theory (CBT), especially for thick beams; for instance, at a span-to-thickness ratio of h/L = 12.5, HSDT predicts increases of approximately 6%, 7%, and 12% in displacement, voltage, and harvested power, respectively, compared to CBT. Parametric studies further reveal that increasing the load velocity significantly enhances the strain rate in the piezoelectric layer, resulting in higher voltage and power output, with the latter exhibiting quadratic growth. Moreover, increasing the material gradation index n reduces the beam’s effective stiffness, which amplifies vibration amplitudes and improves energy conversion efficiency. These findings underscore the importance of incorporating shear deformation and material gradation effects in the design and optimization of piezoelectric energy harvesting systems using FGM beams subjected to dynamic loading. Full article

A new computational framework for nonlinear dynamic analysis of smooth shell structures is presented in this paper. The new framework is based on Simo & Tarnow’s energy–momentum conservation algorithm. A novel co-rotational nine-node quadrilateral shell element is embedded in the new framework. The dynamic equilibrium differential equations are derived using the Hamilton principle and solved by the Newmark algorithm. At each step, midpoint interpolation is applied to both nodal variables and their time derivatives. The average value of strains at the beginning and the end of each step is used to evaluate strain energy to obtain a symmetric tangent stiffness matrix. When deriving the kinetic energy functional, the first-order derivatives of vectorial rotational variables are embedded into equivalent nodal forces. Therefore, a symmetric equivalent mass matrix is generated. The symmetric stiffness and mass matrices significantly reduce the workload in solving the nonlinear governing equations. Benchmark validations reveal close agreement with results in the existing literature. The proposed algorithm is applicable for solving smooth shell structures undergoing large displacements and rotations within spatial domains, while maintaining unconditional stability and geometric exactness. Full article

This study presents a closed-form solution for the dynamic response of a sandwich beam subjected to arbitrary impact loading, with a particular focus on energy harvesting from an attached piezoelectric layer. A thin piezoelectric patch is bonded to the bottom surface of the beam to convert mechanical vibrations into electrical energy. The governing equations of motion are derived using Hamilton’s principle, considering a non-symmetric sandwich cross-section and incorporating higher-order shear deformation effects. The state–space method is employed to obtain the exact dynamic response of the beam under impact excitation. The differential equations governing the output voltage and harvested power are solved analytically based on the derived response. The natural frequencies and dynamic responses are validated against classical beam theory, highlighting the significance of shear deformation. Numerical examples are provided to evaluate the generated voltage and energy harvesting efficiency. The results demonstrate the strong potential for energy harvesting from sandwich beam vibrations and elucidate the influence of impact loading conditions, distributed load amplitude, and the geometric dimensions of the beam on the harvested output. Full article