This paper presents an analytical framework for investigating the stochastic dynamics and stability of an axially moving viscoelastic beam under concurrent transverse magnetic fields, thermal loads, and stochastic excitations. Utilizing the extended Hamilton principle, a nonlinear stochastic governing equation is established that simultaneously incorporates geometric nonlinearities, thermal compressive stress, and magneto‑elastic eddy‑current effects under additive and multiplicative random noises. To handle the hereditary viscoelastic effects, a quasi‑harmonic approximation is introduced, transforming the original system into an equivalent one with effective damping and stiffness. The stochastic averaging method is then applied to derive closed‑form expressions for the probability density functions (PDFs) of the response amplitude and the maximum Lyapunov exponent, providing explicit stability criteria that directly link environmental fields to long‑term system behavior. Parametric studies reveal that axial velocity, magnetic field intensity, temperature increment, and viscoelastic parameters significantly influence both stochastic response and stability, with theoretical predictions validated by Monte Carlo simulations. This work bridges multi‑physics modeling and analytical stochastic tractability, offering a unified stability criterion for axially moving systems in aerospace and mechanical applications.

The normal debonding of the ice-rock interface subjected to dynamic loads with certain frequencies threatens the safety of defense equipment deployed in the polar region. Capturing the frequency of the dynamic load that can excite the debonding behavior on the ice-rock interface cannot be achieved successfully by solving the dynamic model in time domain. The frequency domain generalized multi-symplectic method (FD-GMSM) is developed to reveal the debonding mechanism of the ice-rock interface in this paper. Based on the Hamiltonian variational principle, the ice-rock interaction dynamic model considering the viscoplasticity of the ice, the linear elasticity of the rock, as well as the spring-damping bond property of the interface is established. Then, a FD-GMSM is proposed to perform the high-fidelity simulation of the ice-rock interfacial debonding, which performs the structure-preserving iteration for the dynamic response of the interfacial debonding. Compared to the Fourier transform method (FTM) for time domain integral results, the low simulation cost and the stable multi-symplectic residual of FD-GMSM are presented in the results of the frequency domain simulation. In the simulation, the resonant frequency distribution of the ice-rock system is captured, the significance of which is that, the resonation in the system amplifies the interfacial normal stress to exceed the critical bond strength. The aforementioned results reveal the quadratic nonlinear relationship between the resonant frequency value and its order. Furthermore, the number of the interfacial debonding regions is positively correlated with the order of the resonant frequency, which implies that more interfacial normal stress peaks can be obtained when the excitation frequency equals to a higher order resonant frequency of the system. The verified results reported in this paper imply that, the proposed FD-GMSM can be used to predict the debonding behaviors of the ice-rock interface, which will further be used to guide the site selection of the important defense equipment in the polar region.

In this paper, a piezoelectric energy harvester by exploiting vortex-induced vibration (VIV) under the influence of random wind excitation is designed and the associated nonlinear dynamics is investigated comprehensively. The dynamic equations of motion considering the inherent randomness, including the modified Hartlen-Currie model characterizing the random wind forces, are formulated for the piezoelectric energy harvester. Stochastic averaging method is then employed to derive the stationary distribution of mechanical states, providing insights into the long-term behavior of the system. Both the resonant case and the non-resonant case between Strouhal frequency of incoming wind with the natural frequency of the piezoelectric beam are investigated in detail. Performance metrics, including mean square electric voltage (MSEV) and mean output power (MOP), are theoretically obtained through the analysis. Parameter sensitivity analysis is applied to enhance efficiency, and the results are validated through comparisons with numerical simulation and wind tunnel experiments. The findings from this study offer valuable insights into optimizing the design and enhancing the reliability of piezoelectric energy harvesters under the influence of fluctuating wind conditions.

Bio-inspired thin-walled structures have garnered significant attention for their superior energy-absorption capabilities. This study proposes a novel bionic multi-cell tube (WLMT) inspired by the hierarchical venation of the Victoria Water Lily leaf, integrating Venation Multi-cell Components (VMCs) to enhance crashworthiness. The effects of key geometric parameters, including the number of ribs, on the energy absorption behavior were investigated through theoretical, numerical, and experimental approaches. Results demonstrate that the incorporation of VMCs significantly improves structural performance, increasing specific energy absorption (SEA) by at least 40% compared to conventional multi-cell tubes. The optimal crashworthiness was achieved with a four-rib configuration. A theoretical model for predicting the mean crushing force (MCF) was developed based on the simplified super folding element (SSFE) theory, yielding predictions in close agreement with finite element simulations. Furthermore, multi-objective optimization using the response surface method (RSM) and the NSGA-II algorithm was performed to maximize SEA while minimizing the peak crushing force (PCF), leading to an optimal design configuration. The proposed WLMT exhibits exceptional energy-absorption characteristics, showing great potential for applications in impact protection systems such as high-speed trains.

Tensegrity structure is one of the ideal structural form to realize modular assembly of large spacecraft. Understanding the dynamic characteristics of modular tensegrity structures such as natural frequencies, vibration modes and wave behavior is crucial for the successful deployment of spacecraft in space. In this paper, according to the engineering practice of spacecraft assembly, we choose a regular hexagonal tensegrity structure module, and establish the dynamic model of tensegrity structure based on Lagrangian equation by finite element method and node coordinate vector. Subsequently, the natural frequencies and vibration modes of the modular tensegrity structure during the expansion process are analyzed. It is found that as the number of modules increases, the natural frequency tends to decrease and the torsional mode is more likely to occur. In addition, a comparison is made between the isotropic solid circular plate structure and the tensegrity structure, focusing on differences in modes and frequencies. The influence of self-stress on the modal characteristics and natural frequencies of tensegrity structures with varying numbers of modules is also investigated. Furthermore, according to the Bloch's theorem and the dynamic model, a wave propagation model for the tensegrity structure module units is established, from which the band structure and group velocity are derived. By comparing these results with the wave propagation paths obtained from numerical simulations of the large space tensegrity structure, it is demonstrated that the wave behavior of the large space tensegrity structure can be obtained by analyzing the wave characteristics of the module unit. Moreover, it is revealed that the regular hexagonal prism tensegrity structure exhibits difficulty in transmitting transverse waves and possesses a unique wave propagation directionality.

To address the core contradiction that both low peak collision force (PCF) and high specific energy absorption (SEA) are difficult to balance simultaneously in energy-absorbing structures, and to achieve their synergistic optimization, this study proposes a novel pre-folded double-layer multi-cell tube (PDMT) configuration inspired by origami structures. The incorporation of origami-inspired geometric patterns effectively suppresses initial peak loads, while leveraging the inherent SEA advantages of multi-cell structures. Through a bilayered nested design, this architecture achieves simultaneous optimization of low initial impact force and high energy absorption efficiency. By introducing the in-plane thickness distribution gradient k, the energy absorption capacity of the gradient double-layer multi-cell tube (GDMT) is significantly enhanced compared to that of the PDMT, with the SEA showing a maximum increase of 65.9%. For quantifying the constraining influence of ribs on double-layered tube structures and their enhancement on crashworthiness, the contribution of individual components and the interaction between them to the energy absorption of the GDMT was investigated. It is found that the interaction exerts the most significant influence on the energy absorption of the GDMT. Meanwhile, a multi-objective optimization method was employed to optimize the GDMT, yielding the optimal solution. Its PCF and SEA were 117.8 kN and 26.8 kJ/kg, respectively. The research findings establish a critical theoretical foundation for the crashworthiness structural design of next-generation high-speed trains, provide actionable technical guidance, and offer a new paradigm for the optimal design of origami-inspired multi-cell structures.

Solving partial differential equations (PDEs) with high-frequency solutions remains a central challenge in physics-informed machine learning due to spectral bias – the tendency of neural networks to learn low-frequency components preferentially. This paper proposes a Frequency Shift Physics-Informed Extreme Learning Machine (FS-PIELM) framework that addresses this limitation through an additive mechanism for weight initialization. Rather than multiplying random weights by a scaling factor, the method translates the mean of the Gaussian weight distribution while keeping the variance fixed at unity, thereby avoiding the variance amplification inherent in scaling-based methods. Two variants are developed: FS-PIELM-L assigns independent frequency magnitudes to individual neurons, while FS-PIELM-G groups neurons for improved robustness. Theoretical analysis shows that the frequency variance under the proposed framework remains bounded and approaches unity regardless of target frequency, in contrast to the quadratic growth of conventional approaches. The method preserves the computational efficiency of extreme learning machines, requiring only a single linear solve. Experiments on seven benchmark problems spanning six equation types – Helmholtz, wave, Poisson, Klein-Gordon, heat, and advection-diffusion – on both regular and complex geometries show that the linear variant achieves the best accuracy in six of seven cases, with improvements of one to nearly five orders of magnitude over existing PIELM variants. The code and data accompanying this manuscript will be made publicly available at https://github.com/xgxgnpu/Physics-informed-vibe-coding/tree/main/FS-PIELM.

In this work, a fully coupled second-order nonlinear elastic framework is established via perturbation analysis. This addresses the predictive limitations of current hydrogel models caused by undefined micro-macro correlations and inaccurate phase transition characterizations. A thermo-dependent Flory interaction parameter is incorporated, and closed-form elastic coefficients varying with temperature and chemical potential are derived. A double well free energy landscape is captured to characterize swelling-collapse phase transitions, whose critical conditions are identified through parametric analysis. Thermal modulation of elastic modulus and nonlinear mechanical responses is validated via uniaxial tension simulation and experimental data of poly-(N-isopropylacrylamide) hydrogels. With only five interpretable elastic parameters, the developed framework provides an efficient and reliable tool for multi-field mechanical analysis of responsive hydrogel materials.

As a promising cross-sea infrastructure, the submerged floating tunnel (SFT) relies on anchor cables as its primary load-bearing components, with their dynamic response critically influencing the overall safety and feasibility of the system. Existing studies often employ simplified mechanical models and solution methods, which may fail to accurately capture the nonlinear vibration characteristics of anchor cables. To overcome this limitation, this paper develops a precise and general analytical framework for analyzing the nonlinear vibration of anchor cables, enabling efficient and accurate determination of their free vibration response. First, a Bernoulli–Euler beam model with shallow sag is used to establish the dynamic equation of the anchor cable, incorporating elastic support boundary conditions. Next, the dynamic stiffness method (DSM) is combined with the perturbation method to accurately compute the modal frequencies and mode shapes. Finally, the energy equivalence principle is applied to decouple the nonlinear equations of motion, leading to an analytical solution for the dynamic response. Numerical results confirm that including the first seven modes provides a more accurate representation of the cable's dynamic behavior. The maximum displacement along the cable occurs near its trisection points, while the maximum stress is located close to the upper anchorage. Both the fluid damping coefficient and the structural damping ratio significantly affect the vibration attenuation. The proposed method demonstrates higher computational accuracy and efficiency compared to conventional numerical approaches, effectively balancing analytical precision with engineering practicality.

The magnetic flux variable based on the working principle of magnetic-controlled memristors is introduced to address the electromagnetic induction problem caused by electromagnetic activities inside and outside the nervous system, providing the possibility of exploring electromagnetic regulation of network spatiotemporal behavior from the perspective of neurodynamics. This paper systematically detects the feasibility and effectiveness of electromagnetic stimulation in regulating spiral wave evolution based on a constructed two-dimensional regular neuronal network. After the negative feedback effect of electromagnetic stimulation on neuronal activity is confirmed, the regulation of periodic electromagnetic stimulation on spiral wave dynamics is quantitatively discussed with the help of three network metrics, namely spiking ratio, average membrane potential and average Hamilton energy. The results show that for two different regulatory schemes, the periodic stimulation can induce the drift or disappearance of spiral waves, which can be elucidated through the bifurcations of neuronal dynamics. Particularly, local stimulation makes the stimulated region act as a barrier by inhibiting the neuronal activity, thereby inducing the wave head to drift along a specific path or the spiral pattern to transition into a fascinating double spiral wave. These novel results of constrained drift and transition of splitting into two are first detected, enriching the dynamics of spiral waves and providing clinical guidance.

Traditional Physics-Informed Neural Networks (PINNs) based on multilayer perceptrons face optimization difficulties, spectral bias, and limited parameter efficiency when solving complex fluid dynamics problems. This work addresses these limitations by developing J-PIKAN, a physics-informed Kolmogorov-Arnold Network based on Jacobi orthogonal polynomials.We present a systematic comparison of different basis functions (Jacobi polynomials with various alpha,beta parameters, Chebyshev, Legendre, Hermite, Fourier, B-spline, and Taylor) across five representative fluid dynamics benchmarks. Our comprehensive analysis reveals that Jacobi polynomials consistently achieve superior performance, delivering 1-2 orders of magnitude improvement in solution accuracy compared to baseline MLPs across different equation types. Through Hessian eigenvalue analysis, we demonstrate that J-PIKAN exhibits more favorable optimization characteristics with reduced numerical ill-conditioning during training. For high Reynolds number lid-driven cavity flows, J-PIKAN maintains superior accuracy while requiring only 50 % of the parameters compared to basic MLPs. J-PIKAN offers a promising framework for developing efficient and reliable deep learning-based solvers for fluid dynamics, demonstrating significant improvements in both accuracy and parameter efficiency while addressing numerical stability challenges associated with polynomial-based networks. Code will be made available at https://github.com/xgxgnpu/J-PIKAN upon acceptance of the paper.

Topological phases are governed by lattice symmetries, yet how different symmetry-breaking paths (SBPs) affect topological transitions remains insufficiently understood. Most existing studies rely on a single SBP, and address only one bandgap, limiting independent control of multiple gaps. Here, we investigate multiple isolated Dirac points in a trefoil-knot-modified honeycomb lattice, and show that a single SBP generally inverts all relevant Dirac points simultaneously, whereas the tailored combinations of SBPs enable selective and programmable band inversion at targeted gaps. The excitation-dependent responses reveal strong modal selectivity. This capability is exploited to realize independently controllable multi-channel signal splitting, which is unattainable with a single SBP. The results enable SBPs as an effective design degree of freedom for programmable and reconfigurable topological elastic devices.

T-shaped rigid-flexible combination structure is one of the most common space structure forms. Modeling and analyzing on T-shaped spatial rigid-flexible combination structure are challenging due to two types of coupling effects: one is the orbit-attitude-flexible vibration coupling and another is the rigid-flexible structural coupling. In this paper, the strong coupling dynamic problem involved in the on-orbit operation of the T-shaped spatial structure is considered, which is formulated as an orbit-attitude-flexible vibration coupling dynamic model based on the Hamiltonian variational principle firstly. Inspired by the merit of the symplectic Runge-Kutta method in precisely preserving the global conservation quantities of the system’s planar motion and the advantage of the generalized multi-symplectic method in excellently reproducing the local dissipative characteristics of the flexible component, a structure-preserving iteration method is developed to investigate the coupling dynamic behaviors of the T-shaped spatial structure. Using the structure-preserving iteration method, the influences of damping coefficients and initial conditions (including the initial attitude angle and the initial orbital radial velocity) on the dynamic behavior of the model are investigated in detail. From the numerical results, it can be found that, compared to the damping effect, the initial orbital radial velocity has a more significant impact on the evolutions of the orbital radius and of the attitude angle. According to Kepler’s second law, to further verify the validity of the iteration method, the areas swept by the orbital radius corresponding to the geometric center and the fixed point of the T-shaped structure per unit time are presented in the numerical simulation respectively. It can be found that the areas swept by the orbital radius corresponding to the geometric center (or the fixed point) of the T-shaped structure per unit time are almost invariable, which verifies the validity of the numerical iteration method developed in this paper indirectly. The tiny variations of swept areas result from the influence of the gravitational gradient on the orbit-attitude-vibration coupling dynamic behaviors of the large-scale spatial structure. The main contribution of this work is providing an effective numerical iteration method to reveal the coupling dynamic behaviors of large spatial combination structures, which is expected to provide real-time dynamic response results for the real-time feedback control of large spatial structures.

Modularly assembled tensegrity structures represent a promising paradigm for future large-scale space infrastructure, where tailorable dynamic performance is essential for mission-critical applications. However, conventional hexagonal prism tensegrity systems suffer from insufficient structural stiffness, limiting their practical utility. This study introduces a cable-reinforced hexagonal prism tensegrity by strategically incorporating auxiliary cables baseline topology, significantly enhancing mechanical performance. Through Monte Carlo sampling, a wide range of prestress distributions satisfying self-equilibrium conditions were generated, enabling systematic analysis of the relationship between internal force configurations and structural stiffness. Modal analysis and numerical simulations reveal that the proposed design achieves an 80-128% improvement in structural stiffness, with natural frequency serving as the key metric. Furthermore, strong correlations between cable force summations and modal frequencies were established, highlighting the role of prestress distribution in regulating dynamic behavior. Wave propagation on assembled tensegrity beams demonstrates the ability to simultaneously tailor both fundamental frequency and group velocity via predefined prestress patterns. These findings provide a comprehensive framework for multidimensional control of wave dynamics in modular tensegrity systems, offering significant potential for advanced applications in space-borne structural design and vibration mitigation.

Engineering structures are frequently subjected to multi-directional vibrational excitation, calling for the consideration of multi-directional dynamic coupling and its embodiment in vibration isolation design. This paper introduces a 3D-printed integrated isolator designed to attenuate vibrations in two translational and one rotational directions. The structure comprises rigid rods connected by optimized torsional springs to enable threedirectional vibration isolation. Corresponding models alongside the solving procedure are developed, followed by dynamic analyses and experimental validations. The proposed isolator is shown to entail effective lowfrequency and multi-directional vibration isolation. Vertical direction performance remains robust and amplitude-insensitive, and negligibly affecting the horizontal and rotational directions; whereas horizontal isolation deteriorates under rotational excitation with amplitude-dependent severity and vice versa. The rotational excitation is the primary source of both nonlinearity and static equilibrium position offset. This study offers invaluable insights for designing multi-directional isolators for aerospace and transportation applications.

Aimed at the problems of traditional permanent magnet or liquid-cooled permanent magnet type Electro-Magnetic Acoustic transducer(EMAT),such as large volume,easy demagnetization of permanent magnet at high temperature and difficulty in sustained high temperature detection,a laser coil-only Rayleigh Wave(RW)EMAT detec-tion method for high-temperature-sustained on-line monitoring is proposed.A finite element model for field-circuit cou-pling analysis of the aluminum alloy laser coil-only RW EMAT detection process based on the surface constraint mechanism was established,and the effects of key design parameters such as the excitation coil of the coil-only RW EMAT on the amplitude and wave packet width of the RW detection were analyzed by using orthogonal experimental method,according to which,the optimal design parameter combinations of the coil-only RW EMAT was obtained and verified by experiments.The laser coil-only RW EMAT high-temperature on-line detection system was developed,and the on-line detection experiment of surface crack defects of high-temperature aluminum alloy at 20-500℃was carried out.The results show that the number of wire splitting and coil turns of the receiving coil(meander coil)have a major influence on the received signal amplitude and wave packet width of the coil-only RW EMAT,respectively.The receiv-ing amplitude of the optimized coil-only RW EMAT is increased by 1.67 times.Furthermore,the on-line detection of surface crack defects of 500℃high-temperature aluminum alloy can be realized by using the differential circuit device and matching the width of the laser line light source with the turn spacing of the coil-only RW EMAT coil.The proposed method provides theoretical support and technical guidance for laser coil-only RW EMAT high-temperature on-line non-destructive testing and monitoring.

This work investigates the rectification and size-based sorting of finite-size active particles under the action of an unbiased periodic force in a symmetric periodic channel. By combining theoretical modeling and numerical simulations, we explore the effects of the amplitude and temporal asymmetric parameter of the periodic force, as well as the self-propelled velocity and angular velocity, on the transport properties of particles with different sizes. The results show that the amplitude and temporal asymmetric parameter of the periodic driving force significantly affect the average velocity and rectification direction of active particles. Notably, we observe a current reversal phenomenon where the rectification direction of particles is reversed by adjusting the control parameters. For particles with larger sizes, their rectification direction can undergo multiple reversals. The self-propelled velocity of particles inhibits rectification, and passive particles exhibit stronger directional transport capability than active particles. The angular velocity of particles has no effect on rectification. Importantly, particle size plays a crucial role in their directional transport capability, and under many parameter conditions, particles with larger sizes show stronger directional transport capability. In addition, based on the differences in the rectification directions of particles with different sizes, this work proposes a size-based particle sorting mechanism, which can be used to design microfluidic devices for separating active particles.

We propose an advanced symplectic elasticity approach for the anti-plane fracture analysis of V-notched visco-piezoelectric bimaterials that incorporates damage effects. The Kelvin-Voigt model effectively captures the time-dependent behavior of visco-piezoelectric materials. The dual equation formulated within the Hamiltonian framework is directly derived through the method of separation of variables, enabling analytical solutions for the field variables. The mechanical and electric fields near the notch tip are rigorously expressed as linear combinations of symplectic eigensolutions, facilitating the explicit derivation of intensity factors. Numerical examples systematically examine the influence of Kelvin-Voigt model parameters, damage variables, and loading conditions on the fracture intensity factor. The results establish a robust theoretical foundation for the safe design and reliability assessment of piezoelectric devices.

This study aims to develop an accurate and efficient dynamic modeling framework for tensegrity on-orbit deployment under attitude-flexibility coupling and strongly time-varying spacecraft’s configurations. An energy-preserving matrix perturbation theory is formulated within the dynamic stiffness framework, together with modal-order verification via the Wittrick-Williams count and 2-norm precision control to suppress error accumulation during continuous perturbation updates. The method is validated on a rotating-extending beam benchmark by comparison with theoretical solution, where the first four modal frequencies agree well with the numerical results and the correction mechanism effectively eliminates accumulated error while significantly reducing computational cost. Based on the validated model, the global modal characteristics of the tensegrity are tracked throughout deployment, revealing transitions between symmetric and antisymmetric mode forms. Parametric studies further quantify how cable prestress and the central body’s rotational inertia influence attitude displacement and modal evolution. Using the identified global modes, deployment responses under different thermal flux incidence angles and post-shadow moments are evaluated, and an optimized deployment strategy is derived to enhance stability. Overall, the proposed framework provides a reliable and computationally efficient tool for global-mode tracking and dynamic assessment, offering practical guidance to improve deployment robustness and reliability.