Table of Content

12 October 2026, Volume 47 Issue 10

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On the mechanics of nonlocal lattices using a lattice Green’s function method

Yuhao GONG, Jinxing LIU

2026, 47(10):  2123-2144.  doi:10.1007/s10483-026-3434-8

Abstract ( 18 )   PDF (8883KB) ( 18 )  

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A lattice Green’s function (LGF) framework is proposed to investigate the mechanical properties of nonlocal lattices (NLLs) with periodically distributed dense defects. The novelty lies in extending the periodic LGF (PLGF) to beam lattices and reformulating both dense defects and nonlocal elements as periodic equivalent nodal forces on a perfect counterpart. This enables displacement perturbation, stress redistribution, and long-range interaction among different unit cells (UCs) to be captured without repeated finite element modeling. With the superposition principle, the defective NLL is transformed into its perfect counterpart, and the effective moduli are derived via strain-energy equivalence. The accuracy of the proposed PLGF method in predicting displacement fields and moduli is verified against the finite element method (FEM) results. The effects of nonlocal interactions on deformation, anisotropic moduli, defect toughening, and stress redistribution are analyzed, providing an efficient theoretical tool for designing toughened lattice metamaterials.

Spider-web-inspired structure for low-frequency vibration isolation

Wei ZHANG, Zikun WANG, Chaoran LIU, Xiaoyang SU

2026, 47(10):  2145-2164.  doi:10.1007/s10483-026-3445-7

Abstract ( 10 )   PDF (3690KB) ( 7 )  

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Spiders can easily maintain a stable posture under external disturbances owing to the excellent anti-disturbance capability of spider webs. Drawing inspiration from the intrinsic topological features of the spider web, this paper proposes a biomimetic structure for low-frequency vibration isolation, a capability that remains challenging for traditional isolators. The rods and elastic ropes are utilized to mimic the radial threads and circumferential threads of the spider web to produce negative stiffness, while the repulsive magnets are adopted to produce hardening positive stiffness. Through a nonlinear compensation method, the entire isolator combining the rod-elastic-rope structure and the repulsive magnets is designed to possess quasi-zero-stiffness (QZS) characteristics with high tunability, thereby enabling effective low-frequency vibration isolation. The static analysis and dynamic modeling of the proposed spider-web-inspired (SWI) isolator are carried out to reveal the underlying principle, along with an exploration of its diverse nonlinear dynamic behaviors such as bifurcations and chaos. The vibration isolation performance is then comprehensively investigated, validating the superior low-frequency isolation capability of the SWI isolator.

Self-flipping mechanism of a bistable photoactuated liquid crystal elastomer-magnet beam

Lin ZHOU, Bingyao REN, Haiming CHEN, Xuehui CHEN, Ting GAO, Kai LI

2026, 47(10):  2165-2186.  doi:10.1007/s10483-026-3443-9

Abstract ( 12 )   PDF (4348KB) ( 8 )  

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Photoactuated self-oscillating systems have received increasing attention due to their capability to convert light energy into sustained mechanical motion. Nevertheless, most reported systems exhibit smooth and continuous oscillations, with limited ability to accumulate elastic energy and release it abruptly for burst-like motion. This study proposes a bistable photoactuated liquid crystal elastomer (LCE)-magnet beam composed of a bilayer composite beam, a tip magnet, and two metal blocks. Through the coupling of photothermal contraction and magnetic adhesion, the proposed beam exhibits the autonomous self-flipping behavior without external control. A nonlinear mechanical model is developed to clarify the underlying mechanism, showing that the self-flipping motion results from the competition between the equivalent force induced by LCE contraction and the magnetic adhesion forces from the two metal blocks. Three motion states, namely static, single-flip, and continuous self-flipping states, are identified. Two critical contraction conditions for state transitions are derived analytically, providing criteria for the onset and persistence of self-flipping oscillation. Parametric analysis further shows that key system parameters govern the transition boundaries between motion states and affect the oscillation frequency. The results provide useful insight into the design of photoactuated smart beam structures with self-sustained burst-like periodic motion.

Frequency splitting and vibration evaluation of braided composite toroidal-cylindrical shell with soft coating

Jichuan CAO, Hui LI, Jintong HAN, Xinyu CUI, Haile YAN, Bo YANG, Zeng LIN, Feng ZHAO, Wei SUN, Bangchun WEN

2026, 47(10):  2187-2208.  doi:10.1007/s10483-026-3439-9

Abstract ( 11 )   PDF (11255KB) ( 5 )  

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To facilitate the design of advanced aero-engine casings, a dynamic analysis framework is developed for the first time for the braided composite toroidal-cylindrical shell with soft coating (BCTCS-SC). The effective material parameters are first evaluated, after which high-order strain-displacement relations are established to describe the deformation of the coupled shell structure. The virtual spring method is adopted to model the rigid connection between the two infrastructures and the end constraints. The displacement fields are then approximated by doubly discrete spectral functions, and the governing dynamic equations are derived via the energy method. The proposed model is validated through comparative studies, and the corresponding mode shapes are visualized. Finally, the effects of key structural and material parameters on the natural characteristics, frequency splitting, and modal exchange are analyzed. The results further clarify the suppression effect of soft coating by modifying the equivalent stiffness and damping distribution. This study establishes a theoretical framework and a technical approach for frequency-splitting prediction and vibration-suppression design of coated braided composite coupled structures.

Nonlinear theoretical analysis and experimental validation of configurations implementing vibration absorbing andenergy harvesting

Mengjie SHANG, Weiyang QIN, Mingming SHI, Jianan PAN, Qi LIU, Kuan LU

2026, 47(10):  2209-2232.  doi:10.1007/s10483-026-3438-8

Abstract ( 10 )   PDF (7242KB) ( 5 )  

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To isolate vibration and harness vibration energy simultaneously, this study proposes a novel piezoelectric-electromagnetic hybrid vibration energy harvester (HVEH). In the structural design, this harvester introduces a quasi-zero-stiffness (QZS) mechanism and lever amplification to increase the displacements. In the transforming mechanism, it combines the electromagnetic and piezoelectric mechanisms to improve the energy harvesting efficiency. First, an electromechanical dynamic model of the system is established. A time-frequency domain transformation strategy is introduced to evaluate the nonlinear electrical outputs of the electromagnetic harvester (EMH) under alternating magnetic fields. The harmonic balance method (HBM) with slowly varying coefficients, combined with the arc-length method, is utilized to determine the analytical amplitude-frequency responses. The results are verified with the numerical simulation. Next, the analytical model is used to explicitly reveal the effects of the key system parameters on the performance. Finally, a harvester prototype is fabricated, and the corresponding experiments are performed. The experimental results demonstrate that the system achieves high harvesting efficiency; under a stochastic excitation with a power spectral density (PSD) of 0.07 g²/Hz, the root mean square (RMS) output powers of the EMH and piezoelectric harvester (PEH) reach 1.788 mW and 223 μW, respectively. This study provides an efficient, self-powered solution for structural health monitoring and vibration mitigation in critical engineering infrastructure.

Multi-field coupling characteristics of two-dimensional piezoelectric quasicrystals with an elliptical inclusion

Tangrui LAI, Liangliang ZHANG, Yang LI, Xiang MU, Yang GAO

2026, 47(10):  2233-2256.  doi:10.1007/s10483-026-3437-7

Abstract ( 12 )   PDF (5592KB) ( 3 )  

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With the rapidly increasing demand for strongly coupled multifunctional materials in engineering applications such as high-performance sensors, defect problems in piezoelectric quasicrystals (PQCs) have attracted growing attention. This study investigates the mechanical behavior of a two-dimensional (2D) PQC containing an elliptical inclusion subjected to uniform loading at infinity and a concentrated force applied in the matrix. Based on the Stroh formalism, combined with conformal mapping and analytic continuation techniques, the analytical solutions for the in-plane displacements and stresses are derived. Meanwhile, the correctness of the model is verified through a comparison between the degenerated infinite-plane numerical results and classical reference solutions. Numerical examples are further conducted to systematically analyze the influence of the inclusion geometry and the loading position on the multi-field coupling responses. The results show that the elliptical inclusion significantly alters the spatial distributions of the mechanical and electrical fields, producing strong disturbances near the inclusion boundary. In particular, decreasing the ellipse aspect ratio b/a markedly enhances the local coupling and stress concentration, whereas the circular inclusion exhibits the weakest anisotropy, resulting in relatively smooth field distributions and low stress concentration. These findings indicate that properly utilizing geometric defects can serve as an effective means of tuning multi-field coupling behavior, and this strategy should be fully considered in engineering design.

Targeted energy transfer in a permanent-magnet-based nonlinear energy sink with electromagnetic coupling and active damping for simultaneous vibration suppression and efficient energy harvesting

N. A. SAEED, O. M. OMERA, Lei HOU, Haiming YI, Zeyuan CHANG, S. A. KHALIL, E. M. AWWAD, N. SARHAN

2026, 47(10):  2257-2280.  doi:10.1007/s10483-026-3441-7

Abstract ( 9 )   PDF (5591KB) ( 4 )  

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Within this work, a permanent-magnet-based nonlinear energy sink (PM-NES) integrated with an electromagnetic energy harvester (EH) is introduced for the simultaneous purposes of vibration control and efficient energy harvesting. The system considered comprises the PM-NES oscillating inside an electrical coil that is connected to a variable resistive load, as well as a linear damper, a nonlinear cubic spring, and the targeted harmonically excited linear oscillator (LO). The mathematical model governing the nonlinear oscillation of the coupled subsystems is derived. By applying the complexification-averaging method, the normalized equation of motion is analyzed, and the autonomous dynamical system governing the slow dynamics of the whole system is extracted. The slow invariant manifold (SIM) is constructed, and the conditions for the targeted energy transfer (TET) mechanism as well as the onset of strong modulation response (SMR) are analytically established. The proposed design allows the PM-NES to oscillate under one of three damping regimes: (i) passive damping only when the electromechanical coupling is deactivated; (ii) active frequency-dependent electromechanical damping, arising solely from Lorentz-force interactions between the moving magnet and the coil in the absence of the linear mechanical damper; (iii) mixed damping, resulting from the combined action of both mechanisms. Utilizing the continuation method, we explore the system steady-state dynamics under different damping mechanisms through frequency response curves, time-domain simulations, and bifurcation diagrams. The main findings demonstrate that the PM-NES operating under the purely active damping regime achieves superior vibration attenuation efficiency and enables complete harvesting of the energy trapped by the NES into electrical energy. In addition, it is found that within the damping regime, both the TET mechanism and SMR can be effectively tuned via a simple adjustment of the electrical resistive load, such as using a potentiometer. These results are validated analytically and numerically, showing that the PM-NES under the Lorentz-force damping mechanism alone offers a significant practical advantage over conventional mechanically damped NES designs.

Bistable rigid model inspired by out-of-plane buckling vibration

Jiaxin ZHOU, Haicheng ZHANG, Pengcheng LI, Fangzhi SHI, Daolin XU

2026, 47(10):  2281-2306.  doi:10.1007/s10483-026-3436-6

Abstract ( 8 )   PDF (3415KB) ( 4 )  

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The out-of-plane buckling phenomenon, a prevalent nonlinear effect in structural mechanics, presents significant challenges for theoretical analysis. Inspired by this behavior, a novel simplified rigid dynamic model (RDM) is proposed to qualitatively capture the nonlinear vibration behavior of structures undergoing out-of-plane buckling. The approximate analytical solution and simulation model of the RDM are formulated. The approximate analytical solution is obtained through the harmonic balance method (HBM) and the arc-length continuation method (ALCM). By analyzing the stiffness variations during the buckling process, the nonlinear stiffness and potential energy characteristics of the RDM are thoroughly explored, revealing distinct softening and hardening stiffness behaviors under different parameter configurations. Two potential application scenarios for the RDM are proposed: one under quasi-zero stiffness (QZS) conditions and the other under bistable conditions. A QZS isolator is designed with two RDMs, and its effective low-frequency vibration isolation performance is confirmed through both numerical and analytical methods. Additionally, under the bistable conditions, a dynamic simulation analysis of the RDM is conducted with the ADAMS software. The consistency between the simulation results and the theoretical calculations confirms the correct implementation of the analytical and numerical frameworks. The dynamics of the RDM provide valuable insights for the design of actuators and energy harvesters. This study offers a reference for the simplified analysis of complex models involving out-of-plane bending-torsion buckling, and lays a foundation for potential applications in the structural design of flapping bistable robots and rotating QZS isolators.

Research on the suppression of underwater acoustic radiation of spherical shells using nonlinear energy sinks

Mingsong ZOU, Hao WANG, Hao LI, Yini YANG

2026, 47(10):  2307-2326.  doi:10.1007/s10483-026-3444-6

Abstract ( 12 )   PDF (4080KB) ( 5 )  

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Applying nonlinear energy sinks (NESs) to suppress acoustic radiation from underwater targets represents a cutting-edge research frontier. Accurately predicting the acoustic radiation of underwater targets coupled with NESs is a key challenge. To address this problem, this study investigates an elastic spherical shell to analytically derive the acoustic radiation solutions for underwater targets equipped with NESs in two installation configurations. The system is decomposed into three subsystems: the NESs, the spring-mass oscillator, and the spherical shell. An explicit and highly accurate vibro-acoustic coupling solution is developed by the finite difference method, the Taylor series expansion, and the Newmark method. This approach enables the real-time computation of the system vibration response and underwater radiated sound power. The accuracy and validity of the proposed computational method and program are verified through two numerical case studies. Finally, regarding the NES installed on the spring-mass oscillator, the suppression effect of the NES on the acoustic radiation of the spherical shell is thoroughly analyzed. The calculations reveal two noteworthy phenomena that are closely related to the nonlinear effects of the NES: (i) the NES can effectively suppress the acoustic radiation at the resonant frequency of the mechanical isolation system, but it also induces a superharmonic component at a frequency which is three times the resonant frequency; (ii) the superharmonic frequency is strongly correlated with the resonant frequency, and the dominant superharmonic component no longer exhibits a strict tripling relationship when the excitation frequency deviates from the resonance.

Nonlinear dynamic behaviors of the cable-stayed shallow arch model under continuous traffic loading

Tong HU, Xiaoyang SU, Houjun KANG, Wei ZHANG, Yunyue CONG, Yuewu WANG

2026, 47(10):  2327-2344.  doi:10.1007/s10483-026-3435-9

Abstract ( 10 )   PDF (641KB) ( 6 )  

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As the span of cable-stayed bridges increases, these structures become more susceptible to vibration under various complex loads. To investigate the dynamic behavior of cable-stayed bridges under vehicle loads, this study establishes a cable-stayed shallow arch model subjected to the equivalent sustained moving-force excitation, with the initial configuration of the bridge deck and cable vibration considered. First, the governing equations are derived based on Hamilton’s principle, in which the initial configuration of the shallow arch is characterized by a non-dimensional rise. Subsequently, the governing equations are reduced to ordinary differential equations (ODEs) by the Galerkin discretization, and the method of multiple time scales is used to derive the modulation equations. On this basis, the steady-state frequency-response and force-response curves are obtained. Numerical analysis indicates that the variations in the initial configuration have a significant effect on the nonlinear behavior of the system. Specifically, as the non-dimensional rise increases within the considered parameter range, the response curves exhibit more complex nonlinear characteristics, with new branches emerging alongside more stable solutions, unstable solutions, and bifurcation points.

Performance-enhanced vibration reduction via a grounded inerter-damper quasi-zero-stiffness dynamic vibration absorber

Kexin ZHANG, Da HE, Jiangchuan NIU, Wanjie ZHANG

2026, 47(10):  2345-2368.  doi:10.1007/s10483-026-3442-8

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To enhance the broadband vibration attenuation capability of conventional dynamic vibration absorbers (DVAs), this study presents a grounded inerter-damper quasi-zero-stiffness DVA (GID-QZS-DVA), and conducts a comprehensive analysis on the system dynamic behaviors. A dynamic model of the system is established, and the slowly-varying amplitude harmonic balance method (SVAHBM) is employed to derive the amplitude-frequency (AF) response and stability conditions. The effects of key parameters on the saddle-node (SN) bifurcation boundary and local periodic-solution instability boundary are clarified, and the dynamic transition process of the system toward chaos is analyzed. The results demonstrate that the proposed absorber effectively suppresses the primary system resonance peak, reduces the unstable region, and mitigates the nonlinear phenomena. The parameter optimization based on the particle swarm optimization (PSO) algorithm further enhances its performance. Compared with traditional absorbers and other inerter-based counterparts, the optimized GID-QZS-DVA demonstrates a desirable vibration reduction capability under harmonic excitation, with competitive performance in resonance peak reduction and suppression bandwidth extension.

Numerical study on coalescence dynamics of two droplets in viscoelastic fluid under simple shear flow

Yiran JI, Lei WANG, Xinyue LIU, Fang CHEN

2026, 47(10):  2369-2390.  doi:10.1007/s10483-026-3440-6

Abstract ( 13 )   PDF (3634KB) ( 8 )  

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This paper focuses on the coalescence dynamics of two Newtonian droplets within the viscoelastic fluid under simple shear flow. A two-dimensional (2D) lattice Boltzmann (LB) method is adopted. It integrates the phase field theory to solve the hydrodynamic governing equations for multiphase systems and a lattice advection-diffusion solver to account for the elastic stress tensor. The validity of the numerical method is benchmarked against the analytical solutions and experimental and numerical results for the single-phase Oldroyd-B Poiseuille flow, single droplet deformation under simple shear flow, and effects of two droplets on the liquid film. With the method, the effects of the Deborah number (De), solvent viscosity ratio (β), and capillary number (C_a) on the shear-induced dynamics of double droplets are systematically examined. The results reveal two distinct droplet behaviors, i.e., coalescence and non-coalescence. For constant De, the droplet deformation increases monotonically with C_a. The force and energy analyses show that De affects the deformation and coalescence time by modulating the elastic stresses at the droplet’s two poles. For varying β, only non-coalescence is observed; increasing β suppresses the deformation and migration by reducing the elastic forces and first normal stress difference. In addition, regardless of De, droplets typically coalesce at low C_a and remain separated at high C_a.