Table of Content

07 April 2025, Volume 46 Issue 4

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An origami-inspired nonlinear energy sink: design, modeling, and analysis

Youcheng ZENG, Hu DING, J. C. JI

2025, 46(4):  601-616.  doi:10.1007/s10483-025-3239-6

Abstract ( 75 )   HTML ( 9)   PDF (4477KB) ( 53 )  

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Designing, modeling, and analyzing novel nonlinear elastic elements for the nonlinear energy sink (NES) have long been an attractive research topic. Since gravity is difficult to overcome, previous NES research mainly focused on horizontal vibration suppression. This study proposes an origami-inspired NES. A stacked Miura-origami (SMO) structure, consisting of two Miura-ori sheets, is adopted to construct a nonlinear elastic element. By adjusting the initial angle and the connecting crease torsional stiffness, the quasi-zero stiffness (QZS) and load-bearing capacity can be customized to match the corresponding mass, establishing the vertical SMO-NES. The dynamic model of the SMO-NES coupled with a linear oscillator (LO) is derived for vibrations in the vertical direction. The approximate analytical solutions of the dynamic equation are obtained by the harmonic balance method (HBM), and the solutions are verified numerically. The parameter design principle of the SMO-NES is provided. Finally, the vibration reduction performance of the SMO-NES is studied. The results show that the proposed SMO-NES can overcome gravity and achieve quasi-zero nonlinear restoring force. Therefore, the SMO-NES has the ability of wide-frequency vibration reduction, and can effectively suppress vertical vibrations. By adjusting the initial angle and connecting the crease torsional stiffness of the SMO, the SMO-NES can be achieved with different loading weights, effectively suppressing the vibrations with different primary system masses and excitation amplitudes. In conclusion, with the help of popular origami structures, this study proposes a novel NES, and starts the research of combining origami and NES.

Surface effects on buckling instability and large deformation of magneto-active soft beams

Lu LU, Min LI, Shuang WANG

2025, 46(4):  617-632.  doi:10.1007/s10483-025-3233-8

Abstract ( 48 )   HTML ( 2)   PDF (2470KB) ( 18 )  

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Magneto-active soft materials, composed of hard-magnetic particles embedded in polymeric matrices, have found widespread applications in soft robotics, active metamaterials, and shape-morphing structures across various length scales due to their ability to undergo reversible, untethered, and rapid deformation in response to magnetic actuation. At small scales, surface effects play a crucial role in the mechanical behavior of these soft materials. In this paper, we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field. The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method. By employing the developed theoretical model, parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields. Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength. Specifically, when the magnetic field strength is relatively small, surface effects reduce the deformation of magneto-active soft beams, particularly for beams with smaller thicknesses and larger length-to-thickness ratios. However, when the magnetic field strength is sufficiently large, and the beam's deformation becomes saturated, surface effects have little influence on the deformation. This work uncovers the role of surface effects in the mechanical behavior of magneto-active soft materials, which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.

Dynamic analysis of asymmetric piecewise linear systems

Ruiliang ZHANG, Yongjun SHEN, Xiaotong YANG

2025, 46(4):  633-646.  doi:10.1007/s10483-025-3234-9

Abstract ( 62 )   HTML ( 3)   PDF (1751KB) ( 26 )  

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Piecewise linear systems are prevalent in engineering practice, and can be categorized into symmetric and asymmetric piecewise linear systems. Considering that symmetry is a special case of asymmetry, it is essential to investigate the broader model, namely the asymmetric piecewise linear system. The traditional averaging method is frequently used for studying nonlinear systems, particularly symmetric piecewise linear systems, with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions. However, asymmetric systems inherently exhibit non-harmonic, asymmetric responses, rendering the traditional averaging method inapplicable. To overcome this limitation, this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs. Unlike the traditional method, which assumes a purely harmonic response, the improved averaging method redefines the system response as a superposition of a direct current (DC) term and a first harmonic component. Herein, the DC term can be regarded as the offset induced by model asymmetry. Furthermore, the DC term is treated as a slow variable function of time, with its time derivative assumed to be zero when calculating the steady-state solution, akin to the amplitude and phase in the traditional averaging method. Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method. Leveraging these improved results, the study also examines the parameter effect, stability, and bifurcation phenomena within the amplitude-frequency responses.

Chaotic characteristics for a class of hydro-pneumatic near-zero frequency vibration isolators under dry friction and noise excitation

Zhouchao WEI, Yuxi LI, T. KAPITANIAK, Wei ZHANG

2025, 46(4):  647-662.  doi:10.1007/s10483-025-3243-6

Abstract ( 48 )   HTML ( 3)   PDF (3956KB) ( 18 )  

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Hydro-pneumatic near-zero frequency (NZF) vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized gas pressure is properly adjusted. The nonlinear characteristics of such devices make their corresponding dynamic research involve chaotic dynamics. Chaos may bring negative influence and disorder to the structure and low-frequency working efficiency of isolators, which makes it necessary to clarify and control the threshold ranges for chaos generation in advance. In this work, the chaotic characteristics for a class of hydro-pneumatic NZF vibration isolators under dry friction, harmonic, and environmental noise excitations are analyzed by the analytical and numerical methods. The parameter ranges for the generation of chaos are obtained by the classical and random Melnikov methods. The chaotic characteristics and thresholds of the parameters in the systems with or without noise excitation are discussed and described. The analytical solutions and the influence of noise and harmonic excitation about chaos are tested and further analyzed through many numerical simulations. The results show that chaos in the system can be induced or inhibited with the adjustment of the magnitudes of harmonic excitation and noise intensity.

Coupled thermo-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams

Jianping LIU, Zhaozhong YANG, Liangping YI, Duo YI, Xiaogang LI

2025, 46(4):  663-682.  doi:10.1007/s10483-025-3236-7

Abstract ( 55 )   HTML ( 2)   PDF (6643KB) ( 20 )  

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A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented. Heat exchange between the cold fluid and the hot rock is considered, and the thermal contribution terms between the cold fluid and the hot rock are derived. Heat transfer obeys Fourier’s law, and porosity is used to relate the thermodynamic parameters of the fracture and matrix domains. The net pressure difference between the fracture and the matrix is neglected, and thus the fluid flow is modeled by the unified fluid-governing equations. The evolution equations of porosity and Biot’s coefficient during hydraulic fracturing are derived from their definitions. The effect of coal cleats is considered and modeled by Voronoi polygons, and this approach is shown to have high accuracy. The accuracy of the proposed model is verified by two sets of fracturing experiments in multilayer coal seams. Subsequently, the differences in fracture morphology, fluid pressure response, and fluid pressure distribution between direct fracturing of coal seams and indirect fracturing of shale interlayers are explored, and the effects of the cluster number and cluster spacing on fracture morphology for multi-cluster fracturing are also examined. The numerical results show that the proposed model is expected to be a powerful tool for the fracturing design and optimization of deep coalbed methane.

Free vibration of piezoelectric semiconductor composite structure with fractional viscoelastic layer

Yansong LI, Wenjie FENG, Lei WEN

2025, 46(4):  683-698.  doi:10.1007/s10483-025-3237-8

Abstract ( 43 )   HTML ( 2)   PDF (680KB) ( 13 )  

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In this study, the free vibration of a piezoelectric semiconductor (PS) composite structure composed of a PS layer, a fractional viscoelastic layer, and an elastic substrate with simply-supported boundary conditions is investigated. The fractional derivative Zener model is used to establish the constitutive relation of the viscoelastic layer. The first-order shear deformation theory and Hamilton's principle are used to derive the motion equations of the present problem. The frequency parameter is numerically resolved with the Newton-Raphson method through the eigenvalue equation. The effects of either geometric parameters, carrier density, and electric voltage applied on the surface of the composite structure or the fractional order of the Zener model on both the natural frequency and loss factor are discussed, and some interesting conclusions are drawn. This work will be helpful for designing and manufacturing PS materials and structures.

Flexoelectric energy dissipating mechanism for multi-impact protection

Xiyan ZOU, Huaiwei HUANG, Xiaohu YAO

2025, 46(4):  699-710.  doi:10.1007/s10483-025-3235-6

Abstract ( 48 )   HTML ( 2)   PDF (4380KB) ( 18 )  

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Traditional impact protection structures (IPSs) dissipate impact energy according to the plastic dissipation mechanism, which is only effective for single impacts due to the irreversible deformation of structures. To achieve multi-impact protection, this paper proposes a novel chiral periodic structure with the deformation self-recovery function and the high energy conversion efficiency based on the flexoelectric mechanism. A theoretical model is formulated on the electromechanical responses of a flexoelectric beam under rotational boundaries. The equivalent stiffness and damping characteristics are subsequently derived to construct the electromechanical responses of the structure under constant velocity and mass impacts. Discussions are addressed for the influence of the structural scale effect and resistance on the electromechanical responses. The results show that the energy conversion efficiency increases by 2 to 3 orders of magnitude, reaching as high as 85.3%, which can match well with those of structures reported in the literature based on the plastic energy dissipating mechanism.

A thermoelastic model with two relaxations for the vibration of a microbeam resting on elastic foundations

Z. S. HAFED, A. M. ZENKOUR

2025, 46(4):  711-722.  doi:10.1007/s10483-025-3241-8

Abstract ( 45 )   HTML ( 3)   PDF (680KB) ( 18 )  

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The Euler-Bernoulli (E-B) beam theory is combined with Green-Lindsay's (G-L) generalized thermoelasticity theory to analyze the vibration of microbeams. The frequency control equation, based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams, is presented. This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators. =0.28 em plus 0.1em minus 0.1em The frequencies derived from the present model are compared with those from Lord and Shulman's (L-S) theory. The fourth-order solutions for natural vibration frequencies are graphically displayed for comparison. Therefore, attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.

A low Mach number asymptotic analysis of dissipation-reducing methods for curing shock instability

Hongping GUO, Xun WANG, Zhijun SHEN

2025, 46(4):  723-744.  doi:10.1007/s10483-025-3242-9

Abstract ( 48 )   HTML ( 6)   PDF (413KB) ( 9 )  

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We are intrigued by the issues of shock instability, with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it. For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components, such as a disturbed one-dimensional (1D) steady shock wave, we conduct a formal asymptotic analysis for the Euler system and associated numerical methods. This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms. Furthermore, a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms. To verify the stability mechanism, a consistent, low-dissipation, and shock-stable HLLC-type Riemann solver is presented.

Physical structures of boundary fluxes of orbital rotation and spin for incompressible viscous flow

Tao CHEN, Tianshu LIU

2025, 46(4):  745-762.  doi:10.1007/s10483-025-3238-9

Abstract ( 41 )   HTML ( 2)   PDF (644KB) ( 12 )  

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Vorticity is locally generated on a boundary at a rate measured by the boundary vorticity flux (BVF), which can be further decomposed into the sum of the orbital rotation and the generalized spin (specifically, the sum of shear and streaming vorticity) under the field description. For an incompressible viscous flow interacting with a stationary wall, the full expressions of the boundary fluxes of the orbital rotation and the spin are derived, for the first time, to elucidate their boundary creation mechanisms. Then, these new findings are successfully extended to the study of the boundary enstrophy dynamics, as well as the Lyman vorticity dynamics as an alternative interpretation to the boundary vorticity dynamics. Interestingly, it is found that the boundary coupling of the longitudinal and transverse processes is only embodied in the boundary spin flux, which is definitely not responsible for the generation of the boundary orbital-rotation flux. In addition, the boundary fluxes of enstrophy are directly associated with the boundary source of the second principal invariant of the velocity gradient tensor (VGT) and the two quadratic forms representing the spin-geometry interaction. The present exposition provides a new perspective and an additional dimension for understanding the vorticity dynamics on boundaries, which could be valuable in clarifying the formation mechanisms of near-wall coherent structures and flow noise at the fundamental level.

Simultaneous imposition of initial and boundary conditions via decoupled physics-informed neural networks for solving initial-boundary value problems

K. A. LUONG, M. A. WAHAB, J. H. LEE

2025, 46(4):  763-780.  doi:10.1007/s10483-025-3240-7

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Enforcing initial and boundary conditions (I/BCs) poses challenges in physics-informed neural networks (PINNs). Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems; however, the simultaneous enforcement of I/BCs in dynamic problems remains challenging. To overcome this limitation, a novel approach called decoupled physics-informed neural network (dPINN) is proposed in this work. The dPINN operates based on the core idea of converting a partial differential equation (PDE) to a system of ordinary differential equations (ODEs) via the space-time decoupled formulation. To this end, the latent solution is expressed in the form of a linear combination of approximation functions and coefficients, where approximation functions are admissible and coefficients are unknowns of time that must be solved. Subsequently, the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain. A multi-network structure is used to parameterize the set of coefficient functions, and the loss function of dPINN is established based on minimizing the residuals of the gained ODEs. In this scheme, the decoupled formulation leads to the independent handling of I/BCs. Accordingly, the BCs are automatically satisfied based on suitable selections of admissible functions. Meanwhile, the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients, and the neural network (NN) outputs are modified to satisfy the gained ICs. Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of dPINN compared with regular PINN in terms of solution accuracy and computational cost.