Table of Content

02 March 2026, Volume 47 Issue 3

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Thermal stability design for flexural wave bandgap of metamaterial plates with perforated and pre-curved patterns

Qian GENG, Xing ZHOU, Mengyang WANG, Xiongwei YANG, Zhushan SHAO, Yueming LI

2026, 47(3):  443-472.  doi:10.1007/s10483-026-3359-6

Abstract ( 23 )   PDF (32391KB) ( 5 )  

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A design idea for single-component metamaterial plates is proposed to achieve the thermal stability of flexural wave bandgap by the perforated and pre-curved patterns. The band structure analysis suggests that perforation can release part of the in-plane thermal expansion to weaken the softening effect of thermal stress. Introducing pre-curved components to the perforated structure will stop the decrement of the bandgap frequency in thermal environment, and even make the frequency higher with appropriate structural parameters. The bending stiffness of the heated plate is enhanced by the thermal deflection induced stiffening effect of the pre-curved components. The segmented pre-curved component presents a strong ability to resist the thermal influence on the flexural wave bandgap. A simplified model is established for the local structure of the pre-curved component. The theoretical calculations explain the thermally induced frequency increment of the bandgap and the discrepancy in the thermal response between the two pre-curved models. The transmittance of flexural wave validates the effectiveness of the proposed design.

Synergistic design of ultra-wide low-frequency continuous bandgap metastructure for audible noise attenuation

Dongxu GUO, Xiaolong ZHANG, Ruilan TIAN, Xiangyang LI, Minghao WANG

2026, 47(3):  473-496.  doi:10.1007/s10483-026-3361-7

Abstract ( 11 )   PDF (19692KB) ( 2 )  

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Local resonant acoustic metamaterials have broad applications in sound insulation, yet their single-configuration designs often exhibit limited and discontinuous bandgap widths, hindering full-frequency noise attenuation across the human auditory range. This study presents a double-phase fidget-spinner-shaped acoustic metamaterial (DFAM), specifically designed to achieve an ultra-broad, low-frequency continuous bandgap by means of synergistic structural optimization, enabling effective and robust control of audible noise. Based on Bloch’s theorem and the finite element method, the dispersion relation of the DFAM structure is calculated and verified by the transmission loss curves. The propagation characteristics of sound waves within the structure are further analyzed for noise frequencies that fall within the passband. The influence of the geometric and physical parameters on the bandgap is investigated, and the corresponding transmission loss in the propagation direction is further calculated. A hybrid collaborative design strategy, leveraging multi-parameter optimization and bandgap complementarity, is developed to construct a metastructure with continuous bandgap coverage from 20 Hz to 1 000 Hz. The resulting metastructure demonstrates exceptional broadband noise attenuation, achieving a total bandgap width of 876.3 Hz (87.63% of the target range) with the transmission loss up to -762.78 dB in a three-periodic arrangement. The simulation and experimental results for the transmission loss of the DFAM metastructure show strong agreement in the low-frequency range. This work provides a novel framework for designing ultra-wide low-frequency continuous bandgap metastructures, offering significant potential for noise mitigation in complex environments.

Topological transition enabled by composite symmetry-breaking paths in trefoil-knot honeycomb lattices

Tai REN, Xiuhui HOU, Tingting WANG, Zhiwei ZHU, Kai ZHANG, Zichen DENG

2026, 47(3):  497-508.  doi:10.1007/s10483-026-3364-6

Abstract ( 9 )   PDF (17394KB) ( 1 )  

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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.

Singular closed orbits and chaotic behavior of a double-winged quasi-zero-stiffness system

Xinyi HUANG, S. LENCI, Qingjie CAO

2026, 47(3):  509-534.  doi:10.1007/s10483-026-3362-8

Abstract ( 9 )   PDF (21418KB) ( 2 )  

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The complex chaotic behavior of a quasi-zero-stiffness (QZS) double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations. The analysis reveals the coexistence of multiple attractors. As a key mass parameter varies, the mechanism underlying degenerate singular closed orbits is elucidated, based upon which five distinct types of singular closed orbits are discovered, exhibiting both smooth and discontinuous (SD) characteristics. The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations. The numerical results further demonstrate the coexistence of SD motions. For zero damping systems, the Kolmogorov-Arnold-Moser (KAM) structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions. These findings advance the understanding of chaotic dynamics in non-smooth multi-well impact systems.

Constitutive modeling of solvent plasticization and physical aging in glassy polymers

Xu CAO, Kerong WU, Ji LIN, Rui XIAO

2026, 47(3):  535-554.  doi:10.1007/s10483-026-3355-9

Abstract ( 9 )   PDF (509KB) ( 3 )  

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Glassy polymers are widely used in biomedical applications in a solvent environment, yet their long-term performance is governed by the competing effects of physical aging and solvent-induced plasticization. Here, we develop a constitutive model that explicitly couples the solvent concentration, structural relaxation, and mechanical response. This framework is built on a multiplicative decomposition of deformation and an Eyring-type flow rule, with structural evolution described by an effective temperature. A generalized shift factor is introduced to quantify how the solvent concentration and effective temperature jointly affect the relaxation time, thereby integrating physical aging and plasticization. The model is subsequently applied to methacrylate (MA)-based copolymer networks immersed in phosphate-buffered saline for up to nine months. Simulations accurately capture key experimental features, including the strong softening of highly swellable networks, the partial recovery due to aging, and the mitigating role of hydrophobic crosslinking in reducing solvent uptake. While the current single-mode description cannot reproduce the full relaxation spectrum, it establishes an efficient framework for predicting the long-term mechanical performance under coupled environmental and mechanical loading. This study provides a constitutive description of solvent-swollen glassy polymers, offering mechanistic insight into the interplay between plasticization and aging. Beyond biomedical MA networks, this framework establishes a foundation for predicting the long-term performance of polymer glasses under coupled aqueous environmental and mechanical loading.

Generalized semi-analytical modeling of three-dimensional contact responses in piezoelectric semiconductors with conductive indenters

Ling WANG, Huoming SHEN, Yuxing WANG

2026, 47(3):  555-572.  doi:10.1007/s10483-026-3358-8

Abstract ( 11 )   PDF (509KB) ( 1 )  

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Piezoelectric semiconductor (PSC) materials exhibit strong electromechanical coupling affected by free carriers, which makes their contact behavior essential for sensors, actuators, and electronic devices. Analytical models for three-dimensional (3D) PSC contact problems are still scarce, especially for conductive indenters. This work develops a semi-analytical framework to study the 3D frictionless contact between a conductive indenter and a PSC half-space. Fundamental solutions under a unit force and a unit electric charge are derived, and the corresponding frequency response functions are combined with a discrete convolution-fast Fourier transform (DC-FFT) algorithm to achieve an efficient semi-analytical contact model. The numerical results demonstrate that an increase in the surface charge density reduces the indentation pressure and modifies the electric potential distribution. A higher steady carrier concentration enhances the screening effect, suppresses the electromechanical coupling, and shifts the system response toward purely elastic behaviors. The sensitivity analysis shows that the indentation depth is dominated by the elastic constants, while the electric potential is mainly affected by the piezoelectric coefficient. Although the analysis is carried out with spherical indenters, the model is not limited to a specific indenter shape. It provides an effective tool for investigating complex 3D PSC contact problems and offers useful insights into the design of PSC materials-based devices.

The adhesive interlayer effect on the thermoelectric structure with multiple electrodes

Xiaojuan TIAN, Yueting ZHOU

2026, 47(3):  573-598.  doi:10.1007/s10483-026-3363-9

Abstract ( 11 )   PDF (4016KB) ( 3 )  

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Driven by the trend of device miniaturization and high-density integration, the interaction between adjacent electrodes has become a critical factor affecting the interfacial reliability of thermoelectric (TE) structures. This study investigates the influence of adjoining electrode interactions on the interfacial response of a multi-electrode/TE substrate structure, including interfacial stresses and stress intensity factors at the electrode ends. To solve the corresponding boundary-value problem, the Fourier transforms are adopted to derive a governing integro-differential equation for the interfacial shear stress in multi-electrode systems, incorporating the TE effects as generalized forces on the right-hand side. The results show that both the interfacial tension and transverse stress in the electrodes are significantly affected by the presence of adjacent electrodes. The interaction between neighboring electrodes diminishes as their spacing increases or when an adhesive interlayer is introduced. Furthermore, the softer and thinner electrodes, the softer and thicker adhesive interlayer, and the smaller TE loads are found to be beneficial for improving the interfacial performance. These findings may contribute to the accurate measurement in surface sensors and layout design of multi-point health monitoring systems for TE structures.

A novel dual-hardening viscoelastic-plastic constitutive model for thermoplastic resins

Feiyang ZHAO, Jinzhao HUANG, Shangyang YU, Jikai YU, Licheng GUO

2026, 47(3):  599-622.  doi:10.1007/s10483-026-3354-8

Abstract ( 11 )   PDF (7830KB) ( 2 )  

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This study examines the viscoelastic-plastic behavior of thermoplastic resin poly-ether-ether-ketone (PEEK) under high temperature and strain rate conditions, highlighting its potential in aerospace applications due to its impact resistance. A dual-hardening constitutive model that combines physical and phenomenological approaches is developed to simulate the mechanical behavior of PEEK. The model explicitly incorporates its marked tension-compression asymmetry in plasticity and relaxation, along with thermal softening at high strain rates, enabling accurate predictions over a wide range of temperatures and strain rates with minimal parameters. This study establishes a comprehensive workflow from experimentation to finite element (FE) simulation for thermoplastic resins. Uniaxial tensile and compression tests (23 °C–180 °C, 0.002 29 s^-1–0.193 61 s^-1) and split Hopkinson pressure bar (SHPB) tests (1 094.08 s^-1–5 957.88 s^-1) are performed to capture stress-strain responses across various conditions, with small-scale specimens enhancing fracture strain measurement accuracy, and quantify the Taylor-Quinney factor of the PEEK material during the adiabatic heating process. The findings demonstrate that the proposed constitutive model effectively predicts yield points across different strain rates and temperatures, with parameters easily obtainable through simple experimental methods, enhancing its practical applications.

Fundamental solutions for two-dimensional piezoelectric quasicrystals with polygonal holes

Tangrui LAI, Xiaoyu FU, Xiang MU, Liangliang ZHANG, Yang GAO

2026, 47(3):  623-638.  doi:10.1007/s10483-026-3356-6

Abstract ( 11 )   PDF (386KB) ( 1 )  

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This paper investigates the mechanical behavior of two-dimensional (2D) piezoelectric quasicrystals (PQCs) containing polygonal holes under external forces. Based on the linear elastic theory of quasicrystals (QCs), the analytical solutions for the stress and displacement fields are derived with the Stroh formalism, Green’s function method, and polygonal mapping functions. Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution. The results show that the polygonal hole shapes significantly influence the generalized hoop stress, with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects. The stress concentrations at hole corners reach their maximum values at specific sharpness parameters, depending on the polygon type. The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs, and provide theoretical guidance for their structural design and optimization.

Temperature-induced frequency activity dips in AT-cut quartz crystal resonators

Nian LI, Chao GAO, Feng CHEN, Zhenghua QIAN, I. KUZNETSOVA

2026, 47(3):  639-652.  doi:10.1007/s10483-026-3360-9

Abstract ( 10 )   PDF (2521KB) ( 1 )  

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This study investigates the frequency-temperature behaviors in AT-cut quartz crystal resonators (QCRs). First, the dispersion relations of an infinite quartz plate are obtained through a semi-analytical finite element (SAFE) analysis, which explicitly reveals the intrinsic frequency-temperature dependence of different vibration modes. Subsequently, we address practical resonator configurations by examining finite quartz plates, where numerical simulations uncover critical interactions between the operational thickness-shear (TS) mode and coupling modes, i.e., the flexure (F), face-shear (FS), and extension (E) modes. Through the frequency spectra analysis, we demonstrate that both the plate aspect ratio and thermal variations affect mode-coupling behaviors. Unstable frequency-temperature variations (activity dips) are observed at critical resonator dimensions. Validation through the free-vibration eigen-frequency analysis and forced-vibration admittance characterization confirms the stable or unstable states predicted by the frequency spectra. The established framework not only reveals the origin of temperature-induced activity dips but also provides the crucial design criteria for suppressing the mode-coupling interference in high-stability resonators.

Study on the influence of internal bearing parameters on the critical speed and vibration behavior of the rotor-bearing coupled system

Fanyu ZHANG, Yulai ZHAO, Qingyu ZHU, Xiangyu MENG, Junzhe LIN, Qingkai HAN

2026, 47(3):  653-674.  doi:10.1007/s10483-026-3357-7

Abstract ( 11 )   PDF (3944KB) ( 3 )  

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The dual challenges of critical speed prediction inaccuracies and ambiguous vibration behaviors are present in high-speed flexible rotors, particularly in free turbine rotors in turboshaft engine systems. The study begins with an examination of the rotor-bearing bidirectional coupling mechanism, with a primary focus on the nonlinear characteristics of the bearing. An investigation is carried out on the mechanical modeling methodologies for four-point contact ball bearings (FPCBBs) and cylindrical roller bearings (CRBs). To address the issue of excessive computational time in traditional bearing calculation methods, the sled dog optimization (SDO) algorithm is substituted for the conventional Newton-Raphson method. A rotor-bearing coupling dynamics model is developed by the finite element and lumped mass methods, with experimental validation achieved through a simulator test rig. The effects of three internal bearing parameters in FPCBBs (arching width and raceway groove curvature coefficient) and CRBs (initial radial clearance) on the critical speed characteristics and vibrational behavior of rotor-bearing coupled systems are examined. The numerical simulation results show some interesting conclusions.