In order to explore the vibration isolation performance of semi-active suspension based on self-powered Magneto-Rheological (MR) damper with interval uncertainty, the electromechanical coupling dynamic model of quarter vehicle suspension with key parameters perturbation is established. The vibration isolation capability is investigated in time and frequency domain with key parameters perturbation respectively. The non-probabilistic reliability of the proposed suspension is deduced by shortest distance method. The balance index reflecting the comprehensive performance of energy harvesting characteristic and vibration isolation capability simultaneously is proposed by dynamical programming theory. The adjustment of structural parameters of damper is much more effective to improve the comprehensive performance. The optimized key parameters are obtained by calculating the Nash equilibrium point of the balance index, meanwhile, the validation of the proposed optimized approach with NSGA-II algorithm is conducted. The optimized MR damper and energy harvesting part are fabricated and tested. The experimental results are similar to the simulating results, which indicates the effectiveness and correctness of the proposed optimized method.

With the rapid advancement of intelligent electromechanical systems and micro/nano engineering technologies, nanoscale magneto-electro-elastic phononic crystal (MEE-PC) plates have attracted significant attention in micro-/nano-acoustics and vibration control due to their superior elastic wave manipulation capability and flexible active tunability. Nevertheless, current research on bandgap characteristics of nanoscale MEE-PC plates still has limitations. The bandgap regulation mechanism involving nonlocal effects and multiphysical-field coupling remains unclear, and effective schemes for collaborative optimization of external field parameters are also lacking. To address these issues, the multiphysical-field-coupled wave governing equations are established based on Kirchhoff thin plate theory and Eringen’s nonlocal elasticity theory. The plane-wave expansion (PWE) method is subsequently employed to calculate the band structures of periodic MEE-PC plates. The effects of nonlocal parameters, prestress, magnetic potential, and applied voltage on the bandgap position and bandwidth are systematically investigated. Furthermore, a particle swarm optimization (PSO) algorithm is introduced to achieve coordinated optimization of multiple external physical-field parameters with the objective of maximizing the first bandgap width. The optimized parameter combination increases the first bandgap width from 17 to 81.2 GHz, representing an enhancement of approximately five times. Sensitivity analysis and repeated independent experiments further confirm the robustness and reliability of the proposed optimization strategy. The results reveal that nonlocal effects play a critical role in the evolution of high-frequency bandgaps, while external multiphysical fields provide an efficient and flexible approach for active bandgap manipulation. This study provides theoretical guidance for the design and optimization of intelligent vibration-control systems and micro-/nano-acoustic devices.

The nonlinear characteristics of flexible-joint robotic manipulators (FJRMs)—namely “joint flexibility–coupling–vibration”—have become a primary bottleneck that limits the realization of high-precision operation and safe human–robot collaboration in industrial, aerospace, service, and medical applications. To systematically summarize the main threads and frontier advances in dynamics modeling in this field, this paper analyzes 1180 related publications indexed in the Web of Science database from 2000 to 2025 and employs bibliometric methods to critically interpret the developmental trajectory and global research landscape. On this basis, key modeling approaches for FJRMs are reviewed from two complementary perspectives: physics-based mechanisms and artificial intelligence, with an in-depth assessment across multiple dimensions. For physics-based modeling, we examine modeling methods for flexible-joint structural representations and major nonlinear factors—such as friction, backlash, and transmission error—and summarize strategies for coupled modeling under joint-and-link dual flexibility. For AI-based modeling, we trace the evolution from classical neural networks to physics-prior-driven paradigms and clarify both the strengths and challenges of data-driven approaches in fitting complex dynamics. By comparing the principal characteristics, advantages, and limitations of these two categories, we argue that physics–data fusion modeling is a critical direction for balancing accuracy and efficiency in future developments. Finally, we discuss emerging trends in unified modeling frameworks, online evolutionary capability, and system-level intelligence, thereby providing theoretical references for high-performance control and engineering applications of FJRMs.

A flexible link manipulator with bilateral cable stiffening is given. The flexible link manipulator is simulated as an Euler-Bernoulli beam, and the cables are assumed to be two springs with negligible mass, and the dynamics of the stiffened flexible link manipulator is modelled by the Hamilton's principle. In order to control the residual vibration at the end of the flexible link manipulator, a boundary control strategy considering the cable parameters is proposed. The vibration characteristics and boundary control measurements of the double cable-stiffened flexible link manipulator are investigated, and the results show that the proposed boundary control strategy can quickly suppress the residual vibration at the end of the flexible manipulator and joint of the manipulator can move to the specified position accurately.

For suppressing multidimensional vibration effectively, the multidimensional vibration isolator based on parallel mechanism considering interval joint clearance is proposed. The kinematics and dynamics of the isolator are established respectively. The contact force generated due to interval joint clearance is modeled respectively by the Lankarani–Nikravesh (L-N) model and the modified Coulomb friction force model. Furthermore, the dynamics of the isolator with interval joint clearance are obtained by the first order interval perturbation method. The upper and lower bounds of vibration isolation performance are calculated, which indicates the isolator with interval joint clearance inhibited external vibration in time and frequency domain respectively. The vibration isolation performance is most sensitive in pitch (around x ) direction due to the existence of interval joint clearance. The non-probabilistic reliability model of the isolator is proposed by the shortest distance method, and the non-probabilistic reliability index is investigated in each isolation direction with interval joint clearance. The reliability index of the isolator exhibits a quasi-stable area in horizontal (in x ) and pitch (around x ) directions, which implies the reliability index is not sensitive to joint clearance variation in a certain perturbation range. The proposed vibration isolator with interval joint clearance is fabricated, and the vibration isolation experiment is conducted. The experimental results are generally consistent with the theoretical results, which indicates the correctness of the analysis.

During the milling process, chatter greatly reduces the machining accuracy and efficiency of parts and decreases tool life. In previous studies, the stiffness variation (SV) method has been shown to be effective in suppressing chatter. However, most of the studies on SV for milling did not consider the effect of the modulation phase, and the stiffness excitation was applied in both the x and y directions. Meanwhile, these studies are based on the conventional regenerative effect model, which does not consider the effect of process damping. In order to suppress chatter more accurately and effectively, this paper establishes a milling process model that considers both stiffness variation and process damping, and analyzes the effect of stiffness variation and process damping on milling stability. On this basis, the differential phase stiffness variation (DPSV) method considering phase variation and the unilateral stiffness variation (USV) method considering stiffness modulation in a single direction are proposed. Simulation results show that the enhancement of stability by DPSV and USV is overall better than that of SV. In addition, the effect of different modulation parameters of DPSV and USV on milling stability is analyzed separately. The effectiveness of the proposed chatter suppression methods is verified by time-domain simulation.

Suspension system is an important component to ensure handling capability and comfort of passengers simultaneously. For reusing the energy dissipated by damper, a novel theoretical model of semi-active suspension with energy harvesting characteristics is presented. The actuators of the proposed suspension are Magneto-Rheological (MR) dampers with energy harvesting part. Firstly, the electrical model of self-powered MR damper is established through Kirchhoff’s law. Subsequently, a quarter vehicle suspension mechanical-electrical model is formulated. Due to perturbation values introduced by unmodeled dynamics, such as time-varying input disturbance, unpredictable errors of self-powered MR damper, the system parameters of self-powered semi-active suspension are not known completely. Thus, adaptive optimal fault tolerant control algorithm is proposed to ensure the vibration isolation performance with unmodeled dynamics. The actual damping force is described by efficiency factors, meanwhile the ideal control gain matrix is obtained by solving Riccati equation. The vibration isolation performance of the proposed suspension system is compared with passive control in time and frequency domain respectively. The results indicate that adaptive optimal fault tolerant control is more effective than passive control, which can improve vibration isolation capability of suspension significantly.

PurposeIn order to overcome the limitation of external power supply and complex maintenance of Magneto-Rheological (MR) damper, the MR damper with energy harvesting characteristics is proposed. The output damping force is the key point for energy harvesting MR damper to realize vibration control. Thus, the sensitivity and the contribution of key parameters to output damping force are meaningful to be explored, meanwhile, the contradiction between energy harvesting and vibration isolation performance should be compromised.MethodsFirstly, the electro-mechanical output damping force model of MR damper with energy harvesting characteristics is established by Kirchhoff's law and Bingham model. Subsequently, the electro-mechanical coupling dynamical model of semi-active suspension with energy harvesting characteristics is derived. The sky-hook control algorithm is conducted to eliminate external vibration. The vibration isolation performance is investigated in time and frequency domain respectively. The interval sensitivity analysis approach is conducted to investigate the sensitivity between key parameters of energy harvesting MR damper and output damping force. Furthermore, the orthogonal test approach is employed to determine the contribution of key parameters to output damping force. Finally, a multi-objective optimization is conducted by NSGA-II method to solve the contradiction between energy harvesting and vibration isolation capability.ResultsCompared to passive control, sprung mass displacement root mean square (RMS) value and velocity RMS value of semi-active control are reduced by 72.05% and 38.24% in time respectively. The amplitude of displacement transmissibility of semi-active control decreases about 20dB compared to passive control. The interval sensitivity is increased by the selected key parameters increasing with different growth rate. Through orthogonal test, the contribution of each key parameters to output damping force is obtained. The inner and outer diameter of generating coil make most contribution to output damping force, which are 1260.96 and 878.19 respectively. After multi-objective optimization, the output damping force is increased by 12.31%, and the displacement is reduced by 8.44%.ConclusionsThe sensitivity of key parameters to output damping force is analyzed by interval sensitivity approach. Furthermore, the contribution of key parameters to output damping force is obtained by orthogonal test. The sensitive key parameters are optimized to increase the value of output damping force for improving the vibration isolation performance. The proposed method makes a novel design approach for MR damper with energy harvesting characteristics, which exhibits important practical values.

Harvesting impact energy of raindrops by using piezoelectric energy harvester has become a novel form for powering low-energy consumption devices. During transient impact process, the droplet-structure interaction affects greatly the dynamic response of the harvester by several factors, such as the droplet diameter, the impact velocity and the configuration of piezoelectric structures. In this study, traditional piezoelectric beams are combined with elastic membrane which can improve the flexibility of structural stiffness as well as the electrical output of the harvester. Considering both impact parameters and membrane structural parameters, the impacting force of droplet during impact is modelled by using Gaussian functions and validated by comparing with experimental results. Based on the force model and by comparing simulation results with experimental results, the characteristics of dynamic response are investigated. Results show that the pretension in elastic membrane plays a key role in adjusting the structural stiffness so as the dynamic outputs of the harvester. The coupling effect of elastic membrane and piezoelectric beams provides a fast and effective approach to match with frequency of external excitations by adjusting the membrane pretension without changing the original structure size.

One of the most frequent barriers to decreasing the surface quality of workpieces during milling machining is chatter, and the accuracy of chatter prediction is directly impacted by the number of effects that are considered during the modeling of the milling process. Previous researchers have studied the impact of chatter suppression on the spindle variable rotational speed method in the milling model while considering various effects. The variable rotational speed waveforms primarily focus on the fundamental waveform or a composite of sine waveforms. The study presents a novel method for variable speed control, utilizing a waveform that combines sine and triangular waveforms. The effect of this method on chatter suppression is investigated in a milling dynamics model that considers regenerative, modal coupling, and process damping effects. This novel method overall improves milling stability significantly. The accuracy of the novel method is verified by simulation and experiment. Next, the analysis focuses on the influence of immersion rate, spindle modulation coefficients, and phase difference on stability, based on stability prediction. The choice of these parameters has a direct influence on the ability to suppress chatter.

In this paper, a boundary control scheme based on the partial differential equation (PDE) model is proposed for the vibration control problem of the flexible manipulator with input constraints and external disturbances. Based on the backstepping method, two boundary controllers are designed to stabilize the position loop subsystem and the attitude loop subsystem, respectively, and auxiliary systems based on the smooth hyperbolic tangent function and Nussbaum function are designed in the controllers to deal with the input saturation and external disturbances. The Nussbaum function can overcome the difficulties in controller design and stability analysis caused by the derivatives of smooth hyperbolic tangent functions. The well‐posedness of the closed‐loop system is proven by employing the semigroup theory, and the uniformly bounded stability is proved by Lyapunov direct method. Finally, the performance of the proposed control laws is verified by numerical simulations.

To reuse the energy dissipated by vehicle suspension, a semi-active suspension with a self-powered magneto-rheological damper is proposed. An electromechanical coupling model of self-powered semi-active suspension is established. The energy conversion efficiency is defined and investigated by changing the electrical parameters. By considering unmodeled dynamics and perturbation values, an adaptive optimal fault-tolerant control algorithm is proposed to ensure the vibration-isolation performance. The robust index of the adaptive optimal fault-tolerant control algorithm is constructed using the Lyapunov equation and evaluated by changing the key parameters. The sensitivity of the key parameters to the damping force is investigated using a grey relation analysis approach. Furthermore, multi-objective optimization between the vibration-isolation capability and energy harvesting is conducted. Via analysis, the proposed suspension can harvest more energy near the second resonance range. Compared to passive control and self-powered mode, the adaptive optimal control algorithm mitigates vibration more significantly in the time and frequency domains, respectively, under stochastic excitation. The robust index is most sensitive to inductance and the diameter of the magnetism cylinder. The length of the damping channel and the diameter of the magnetism cylinder influence the sensitivity of key parameters to the damping force most obviously.

针对柔性关节机器人具有不确定性、轨迹跟踪精度低和抖动的问题,提出一种改进模糊自适应补偿的PD控制方法.该方法在原有模糊自适应控制和PD控制的基础上进行改进,采用改进模糊自适应控制对PD控制进行补偿,以提高存在不确定性条件下的关节轨迹跟踪精度并抑制抖动.通过Lyapunov理论证明了系统的稳定性.仿真结果表明:新型控制器具有良好的自适应能力,与传统PD控制和模糊自适应控制相比,新型控制策略显著提高了关节的轨迹跟踪精度并在一定程度上抑制了关节抖动.

Most machining systems such as machine tools and robots are parameter-varying mechanical systems, which show different dynamic characteristics under different parameters. Generally, a large number of modal tests are required for parameter-varying mechanical systems to obtain frequency response functions (FRFs) under different system parameters, which reduces efficiency. Receptance coupling substructure analysis (RCSA) provides ideas for solving such problems. In this study, the generalized RCSA (GRCSA) was proposed. The coupling method of two substructures at arbitrary pairs of nodes was derived, and a more general coupling method of multiple substructures at arbitrary pairs of nodes was further elaborated, which provides a complete set of theories and methods for the modeling and prediction of FRF of general parameter-varying mechanical systems. Based on the derivation process and results of the GRCSA, the parameter-varying mechanical systems are classified into three basic categories: variable interface systems, variable spatial attitude systems, and variable substructure systems. Typical cases of three basic categories in engineering practice were selected for studying, and the prediction models for FRFs of various parameter-varying mechanical systems were derived in detail. The calculation methods for FRF matrices of various substructures and the calibration methods for interface parameters are given. The validity of the prediction models was verified by experiments and simulations. The relative errors of the established prediction models under most system variables are less than 1% for the natural frequency, and the maximum relative error of the prediction models is 3.775% for the natural frequency. Finally, based on the prediction models, the FRFs under different system variables were predicted, and the variation laws of the natural frequencies with the system variables were analyzed. The modeling processes based on the GRCSA for the FRFs of typical parameter-varying mechanical systems are general, and can provide references and ideas for the study of frequency response characteristics of other complex parameter-varying mechanical systems.

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.

For isolating multi-dimensional vibration experienced by vehicle-mounted precise facility, a multi-dimensional vibration isolator based on parallel mechanism with joint clearance is designed and analyzed. The main thrust of this work is establishing kinematic and dynamic equations of the isolator and exploring vibration isolation capability with joint clearance. Firstly, type synthesis of the parallel mechanism with three translations and one rotation is performed. The kinematic and dynamic equations of the isolator with joint clearance are deduced. Subsequently, vibration isolation performance is simulated with different values of joint clearance under harmonic and stochastic excitations in time and frequency domain, respectively. The simulating results demonstrate the proposed isolator with joint clearance inhibit multi-dimensional vibration effectively. The first-order resonance peak is sensitive to the increment in joint clearance. Finally, the proposed multi-dimensional vibration isolator is fabricated. The vibration isolation experiment is conducted. Through experimental results, the isolator reduces multi-dimensional vibration effectively in time and frequency domain. The vibration isolation capability degenerates as the counterweight of moving platform increases.

航空航天领域中的结构常由于高速飞行时的气动加热等因素在内外表面形成明显的温度差异,结构内部也常因此存在温度的梯度分布.为分析含有温度梯度的梁在高频激励下的动力学响应,建立了热梯度梁的能量流模型.首先通过求解热传导方程得到了梁内的温度场.然后考虑温度场对材料属性的影响,确定了梁的物理中性层以消除拉伸-弯曲变形耦合.基于哈密顿原理建立了梁的弯曲变形控制方程,进而得到了梁弯曲变形的波动频散关系.进一步推导得到了周期平均与局部空间平均后梁振动能量密度与能量流之间的关系,通过任意微元体内的能量平衡关系得到了热梯度环境下梁的能量流模型.与基准解的对比表明,建立的能量流模型能得到热梯度梁在高频激励下较为准确的振动能量分布情况.

Plate structures under moving loads are frequently encountered in practical engineering. Over the past decades, the moving-load models for plates are mainly developed for rectangular plates. In this study, an efficient numerical method is developed for triangular and quadrilateral plates, which are the two most representative polygonal plates and also the basic elements to form general polygon plates. To avoid the mismatch between the moving load and nodes that encountered in Finite Element Method (FEM), the entire domain of the plate is firstly mapped into a square domain using the isoparametric shape functions. The domain decomposition method is also introduced to handle the general polygon shaped plates, whereas the penalty function method is adopted to handle arbitrary boundary conditions. The first-order shear deformation theory (FSDT) is used to describe the elastic deflection of the plates, and then the deformation fields in the mapped domain are spatially discretized by using Chebyshev polynomials of the first kind (CPOFK). Afterwards, the governing equations of motion is derived using Lagrange's equation, in which the inertia force, Coriolis force and centrifugal force due to the interactions between the moving load and supporting plates are taken into account simultaneously. The mode reduction method is employed to reduce the dimension of dynamic equations, and then the first-order generalized-α method is used to solve the dynamic response in time domain. Finally, the correctness and efficiency of the presented method are validated from convergence analysis and comparisons.

手持打磨工具振动大,存在多个振动峰,且不同工况振动峰对应的频率不同.动力吸振器是控制窄带振动峰的有效方法,传统的"弹簧—质量"形式动力吸振器频率不易调节,且不能同时对多个频率进行动力吸振.为适应实际工程应用,以频率可调、可多频减振为目标,首先从结构阻抗角度阐述动力吸振器减振原理,然后设计一种适用于手持打磨工具的频率可调悬臂梁式动力吸振器,推导悬臂梁等效刚度阐述频率调节方法,该结构可方便地布置多重动力吸振器.最后结合仿真分析与实验测试对悬臂梁式动力吸振器的实用性进行验证,证明频率可调并取得良好的多频减振效果.

This paper develops a unified method for the vibration analysis of stiffened plate subjected to moving loads traveling along arbitrary paths. The stiffened plate is modeled as the main/secondary built-up structure in which the plate is selected as the main structure, whereas the stiffeners treated as the beam are selected as the secondary structures. The stiffeners are allowed to be arbitrarily distributed in terms of the number, length, location and orientation. The connection joint between the plate and beam is described by considering the motion compatibility conditions at the interface on the basis of the first order shear deformation theory (FSDT). Both the torsion, bending and warping of the stiffeners are taken into account. To deal with the spatial discretization of the displacement field, the displacements of plate are expressed as the expansions of Chebyshev polynomials of the first kind (CPOFK). Penalty function method using artificial springs is used to realize the various boundary conditions. Afterward, the finite-dimensional governing equations of motion are obtained by means of the Lagrange’s equation. To improve the computational efficiency, the mode reduction technique is used to obtain the reduced-order dynamic model. The first-order generalized-α time integration scheme is then employed to solve the reduced-order governing equations of motion in time domain. The convergence and accuracy of the presented method are verified by comparing with Finite Element Method (FEM) and published literature. Finally, the effects of stiffeners, boundary condition, moving speed and inertia interaction on the dynamic response of stiffened plate are examined by parametric studies.