Table of Content

04 February 2026, Volume 47 Issue 2

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Lightweight integrated sound absorbing-insulating metamaterials with low thickness

Weidi XIA, Hongxing LI, Guotao ZHA, Fulin GUO, Chongrui LIU, Fuyin MA

2026, 47(2):  215-234.  doi:10.1007/s10483-026-3352-6

Abstract ( 7 )   PDF (9205KB) ( 9 )  

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This paper proposes two types of integrated sound absorbing-insulating metamaterials with low thickness and efficient sound attenuation in the low-frequency bandwidth, i.e., labyrinth-type metamaterial and multi-order resonator metamaterial. The labyrinth-type metamaterial is designed through spatial dimension transfer, transferring the required dimension in the thickness direction to the planar thin layer. Based on the Helmholtz resonance, the metamaterial achieves noise reduction through the reflection of sound waves and the thermoviscous dissipation of holes and cavities. This mechanism enables its sound insulation performance to produce the same gain effect as absorption, thereby accomplishing the broadband absorbing-insulating integrated design. With a thickness of only 33 mm, it achieves both sound absorption and insulation effects over more than one octave. The multi-order resonator metamaterial has a larger working bandwidth than the labyrinth-type metamaterial. It is designed based on the multi-order resonance absorption mechanism, and consists of 9 different orders of resonator units. The metamaterial obtains a continuous sound absorption coefficient curve in the low-frequency range of 362–1 712 Hz, and possesses high transmission loss (TL) above 346 Hz. In addition, this paper deeply explores the sound absorbing-insulating mechanism through the correlation analysis between the sound absorption coefficient and TL curves. The experimental results verify the continuous and efficient absorption effects of the two metamaterials, as well as their insulation performance that breaks the mass law. In low-frequency engineering applications, the two designed metamaterials demonstrate great potential and value at sub-wavelength dimensions.

Design and analysis of a mechanically intelligent system for biomechanical energy harvesting

Linchuan ZHAO, Zewen CHEN, X. CHEN, Qiuhua GAO, Zhiyuan WU, Ge YAN, Kexiang WEI, E. M. YEATMAN, Guang MENG, Wenming ZHANG, Hongxiang ZOU

2026, 47(2):  235-254.  doi:10.1007/s10483-026-3353-7

Abstract ( 10 )   PDF (10290KB) ( 1 )  

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The rapid advancement of wearable electronic devices has paved the way for a more intelligent and interconnected world. However, ensuring the sustainable energy supply for these devices remains a critical challenge, particularly for specialized populations and professionals in demanding environments, where a lack of power can pose life-threatening risks. Herein, we propose a mechanically intelligent biomechanical energy harvesting approach that adapts to complex human motion excitations, thereby improving the energy harvesting performance. Leveraging a mechanical intelligence mechanism, the energy harvester aligns with human physiological habits, selectively activating or deactivating as needed. The system can also adapt to excitations of varying directions, amplitudes, and frequencies. Furthermore, the string tension helps reduce the impact forces on the knee joint during foot strikes. A theoretical model for the biomechanical energy harvesting system is developed to describe its dynamic and electrical characteristics, and a prototype is fabricated and tested under diverse conditions. The experimental results are in good agreement with the simulation trends, validating the effectiveness of the theoretical model. A test subject running at 8 km/h for 90 seconds can successfully power a smartphone for 20 seconds, demonstrating the viability of self-powered applications. This mechanically intelligent biomechanical energy harvesting method holds a promising solution for the sustainable power supply for wearable electronic devices.

On a broadband vibration isolator with tunable stiffness: from quasi-zero-stiffness to zero-stiffness behavior

N. A. SAEED, Lei HOU, Haiming YI, A. A. SHUKUR, S. M. ALAMRY, S. M. EL-SHOURBAGY

2026, 47(2):  255-282.  doi:10.1007/s10483-026-3351-9

Abstract ( 5 )   PDF (4436KB) ( 3 )  

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A novel vibration isolation system designed for superior performance in low-frequency environments is proposed in this work. The isolator is based on a unique hexagonal arrangement of linear springs, allowing for an adjustable geometric configuration via the initial inclination angle. Based on the principle of Lagrangian mechanics, the equation of motion governing the structural dynamics is rigorously derived. The system is modeled as a strongly nonlinear single-degree-of-freedom dynamical system, loaded with a normalized payload and subject to harmonic base excitation. To analyze the steady-state response, the harmonic balance method is employed, providing accurate predictions of the payload’s vibration amplitude and displacement transmissibility as functions of both the base excitation amplitude and frequency. The analysis reveals a direct relationship between the isolator’s geometric and stiffness parameters and its load-bearing capacity, leading to the identification of three distinct operational regimes. Depending on the unloaded initial inclination angle, the equivalent stiffness ratio, and the payload design configuration, the system can exhibit one of three vibration isolation modes: (i) the quasi-zero stiffness (QZS) isolation mode, (ii) the zero linear stiffness with controllable nonlinear stiffness, and (iii) the full-band perfect zero stiffness. The vibration isolation performance of the proposed structure is thoroughly discussed for all three oscillation modes in terms of frequency response curves, displacement transmissibility, and time-domain responses. The key novel finding is that this structure can operate as a full-band, high-performance vibration isolator when the initial inclination angle is designed to be a right angle, enabling full isolation of the maximum possible payload. Moreover, the analytical results and numerical simulations demonstrate that the isolator’s displacement transmissibility T with the unit dB tends to -\infty as the air-damping coefficient approaches zero, enabling ideal vibration isolation across the entire excitation frequency range. These analytical insights are validated through comprehensive numerical simulations, which show excellent agreement with the theoretical predictions.

Accurate simulation for strength-degrading effects of geomaterials via a decoupling approach to treating tension-compression asymmetry

Quanpu LIU, Haonan HE, Siyu WANG, Lin ZHAN, O. BRUHNS, Heng XIAO

2026, 47(2):  283-302.  doi:10.1007/s10483-026-3348-6

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This study focuses on a new and high-efficiency approach in a unified sense of accurately simulating strength-degrading effects for geomaterials, including non-symmetric hardening-to-softening effects in tension and compression as well as non-symmetric tensile and compressive stiffness-degrading effects during unloading. It is intended to bypass both modeling and numerical complexities involved in existing approaches. To this goal, new elastoplastic equations are established with new numerical techniques. With a decoupling technique of treating tension-compression asymmetry, the foregoing complex effects are automatically incorporated as inherent response features of the new elastoplastic equations, thus bypassing usual modeling complexities. A new numerical technique of renormalizing piecewise spline functions is introduced to resolve the central yet tough issue of obtaining accurate and unified expressions for the tensile and compressive strength functions, thus bypassing usual numerical complexities and uncertainties in treating numerous unknown parameters and multiple ad hoc criteria. As such, the new approach is not only of wide applicability for various geomaterials but also of high computational efficiency with no more than three adjustable parameters. Toward validating the efficacy of the new approach, numerical examples for granite, salt rock, and sandstone-concrete combined body as well as plain concrete, high-performance concrete, and ultrahigh-performance concrete are presented by comparing model predictions with multiple data sets for strength-degrading effects in tension and compression.

Static and dynamic responses of a piezoelectric semiconductor beam under different boundary conditions

Guoquan NIE, Zhiwei WU, Jinxi LIU

2026, 47(2):  303-324.  doi:10.1007/s10483-026-3345-8

Abstract ( 13 )   PDF (1961KB) ( 7 )  

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Due to the intrinsic interaction between piezoelectric effects and semiconducting properties, piezoelectric semiconductors (PSs) have great promise for applications in multi-functional electronic devices, requiring a deep understanding of the multi-field coupling behavior. This work investigates the free vibration and buckling characteristics of a PS beam under different mechanical boundary conditions. The coupling fields of a PS beam are modeled by combining the Timoshenko beam theory for mechanical fields with a high-order expansion along the beam thickness for electric fields and carrier distributions. Based on the hypothesis of small perturbation of carrier density, the governing equations and boundary conditions are derived with the principle of virtual work. The differential quadrature method (DQM) is used to solve the boundary-value problem. The analytical solutions for a simply supported-simply supported (SS) PS beam are also obtained for verification. The convergence and correctness of the solutions obtained with the DQM are first evaluated. Subsequently, the effects of initial electron density, boundary conditions, and geometric parameters on the vibration and buckling characteristics are explored through numerical examples, where the finite element simulations are also included. The interaction mechanism of multi-physics fields is revealed. The scale effect on the static and dynamic responses of a PS beam is demonstrated. The derived model and findings are useful for the analysis and design of PS-based devices.

Size effect on the thermal fracture behavior of collinear interface cracks in functionally graded coating/substrate structures

Huameng WANG, Zhangna XUE, Jianlin LIU, Z. T. CHEN

2026, 47(2):  325-346.  doi:10.1007/s10483-026-3342-9

Abstract ( 4 )   PDF (1614KB) ( 3 )  

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When micro/nano-scale gradient coatings are subject to large thermal gradients or high heat fluxes, the spatial size effect cannot be ignored. It is important to understand how the size effect influences the thermal fracture behavior of functionally graded coating/substrate structures. This study aims at analyzing the transient thermal fracture behavior of collinear interface cracks in functionally graded coating/substrate structures based on the nonlocal dual-phase-lag heat conduction model. By means of integral transform techniques, the mixed boundary problem is transformed into a set of singular integral equations, which are solved by the Chebyshev polynomials. The effects of the nonlocal parameter, coating thickness, crack spacing, and non-homogeneous parameters on the temperature and stress intensity factors (SIFs) are examined. The numerical results show that these parameters play an essential role in controlling the thermal fracture behavior of the structures, especially at micro/nano-scales.

Electro-mechanical-carrier coupling model in fractured piezoelectric semiconductor strip with vertical cracks

Cai REN, Kaifa WANG, Baolin WANG

2026, 47(2):  347-368.  doi:10.1007/s10483-026-3343-6

Abstract ( 7 )   PDF (2091KB) ( 4 )  

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Understanding the fracture behavior of vertical cracks in piezoelectric semiconductor (PS) structures is vital due to their impacts on device reliability. This study establishes a model for a PS strip with a vertical crack under combined mechanical and electric loading, considering both central and edge cracks. Using Fourier transforms and dislocation density functions, the Mode-III problem is converted to Cauchy-type singular integral equations. The crack surface fields, intensity factors, and energy release rate are derived. The accuracy of the proposed model is verified through the finite element (FE) simulation via COMSOL Multiphysics. The results for low electron concentrations align with those of the intrinsic piezoelectric materials, validating the correctness of the present model as well. The combined effects of crack position, applied electric loading, and initial carrier concentration on the crack propagation are analyzed. The normalized electric displacement factor shows heightened sensitivity to crack size, electromechanical loading, and carrier concentration. The crack position significantly influences the crack surface fields and normalized intensity factors due to the boundary proximity effect.

Locally resonant plate model considering the rotation coupling effect

Hefan DONG, Linjuan WANG

2026, 47(2):  369-388.  doi:10.1007/s10483-026-3344-7

Abstract ( 5 )   PDF (3198KB) ( 2 )  

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In this paper, a theoretical model is established for locally resonant plates with general resonators, and the corresponding governing equation is derived. The model provides a mathematical demonstration of the locally resonant effect, which contains two parts: the first part is induced by translation coupling, and the second part is induced by rotation coupling. The second part cannot be reflected by most existing theoretical models. The analytical solutions of the dynamic response are compared with the direct numerical simulation (DNS) results for two locally resonant plates with different resonator types, thereby validating the general applicability of the present model. The rotation coupling effect leads to the frequency-dependent effective rotational inertia density and anisotropic dispersion relation of the locally resonant plate, as well as the enhancement of the structural vibration suppression ability.

Data-driven early warning of Gaussian white noise-induced critical transitions

Ruifang WANG, Minhe JIA, Xuanqi FAN, Jinzhong MA, Yong XU

2026, 47(2):  389-400.  doi:10.1007/s10483-026-3346-9

Abstract ( 7 )   PDF (242KB) ( 2 )  

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Many complex systems are frequently subject to the influence of uncertain disturbances, which can exert a profound effect on the critical transitions (CTs), potentially resulting in catastrophic consequences. Consequently, it is of uttermost importance to provide warnings for noise-induced CTs in various applications. Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem, this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system. Using the extended dynamic mode decomposition (EDMD) algorithm, we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator. Subsequently, the drift parameters and the noise intensity within the system are identified from the simulated data. Utilizing the identified system, the parameter-dependent basin of the unsafe regime (PDBUR) is quantified, enabling data-driven early warning of Gaussian white noise-induced CTs. Finally, an error analysis is carried out to verify the effectiveness of the data-driven results. Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.

Motion characteristics of a flexible self-propelled slender particle in a backward-facing step flow

Yeyu CHEN, Zhenyu OUYANG, Zhaowu LIN, Jianzhong LIN

2026, 47(2):  401-422.  doi:10.1007/s10483-026-3349-7

Abstract ( 7 )   PDF (12028KB) ( 1 )  

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This study investigates the motion behavior of a slender flexible particle in a backward-facing step (BFS) flow using the direct-forcing fictitious domain method, with a particular focus on the trapping phenomena near the separation vortex region. Three distinct motion modes are identified: periodic rotation or oscillation within the vortex (trapping), downstream transport (escape), and transition state exhibiting unstable trapping. A dynamic balance among inward migration, centrifugal effects, wall interactions, and elastic forces enables the particle to achieve stable orbital motion within two distinct limit cycles. The topology of these orbits is governed by parameters, including the aspect ratio, structural flexibility, deformation intensity, and fluid inertia, all of which are characterized by the Reynolds number (Re). Specifically, fluid inertia plays a dominant role in facilitating particle trapping. At a fixed Re, a particle with a smaller aspect ratio tends to migrate inward and become trapped, whereas one with a larger aspect ratio is more likely to escape. Structural flexibility, especially when enhanced by confinement near the wall, leads to elastic deformation that induces secondary vortices and a weak flipping motion. The deformation intensity \alpha significantly influences the lateral migration of the slender particle after the initial release; a larger \alpha causes it to drift toward the channel centerline, increasing the probability of escape. These findings provide a theoretical foundation for optimizing the transport and capture of slender soft swimmers in complex flow environments.

Neural boundary shape functions in physics-informed neural networks for discontinuous and high-frequency problems

P. T. NGUYEN, K. A. LUONG, J. H. LEE

2026, 47(2):  423-442.  doi:10.1007/s10483-026-3350-8

Abstract ( 5 )   PDF (6130KB) ( 1 )  

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Physics-informed neural networks (PINNs) have been shown as powerful tools for solving partial differential equations (PDEs) by embedding physical laws into the network training. Despite their remarkable results, complicated problems such as irregular boundary conditions (BCs) and discontinuous or high-frequency behaviors remain persistent challenges for PINNs. For these reasons, we propose a novel two-phase framework, where a neural network is first trained to represent shape functions that can capture the irregularity of BCs in the first phase, and then these neural network-based shape functions are used to construct boundary shape functions (BSFs) that exactly satisfy both essential and natural BCs in PINNs in the second phase. This scheme is integrated into both the strong-form and energy PINN approaches, thereby improving the quality of solution prediction in the cases of irregular BCs. In addition, this study examines the benefits and limitations of these approaches in handling discontinuous and high-frequency problems. Overall, our method offers a unified and flexible solution framework that addresses key limitations of existing PINN methods with higher accuracy and stability for general PDE problems in solid mechanics.