Table of Content

17 September 2026, Volume 47 Issue 9

Previous Issue   

Tunable multi-frequency topological waveguiding and demultiplexing in a hexagonal pendant-type acoustic metamaterial

Zhenyu CHEN, Wenwu LU, Guifeng WANG, Ruohan WU, Cheng LI, C. W. LIM

2026, 47(9):  1879-1900.  doi:10.1007/s10483-026-3433-7

Abstract ( 16 )   PDF (3473KB) ( 7 )  

References | Related Articles | Metrics

Multi-frequency topological wave transport has been demonstrated in various acoustic and elastic metamaterial systems. However, realizing independently tunable multi-frequency acoustic channels within a single acoustic metadevice remains challenging, particularly when different topological bandgaps need to be selectively opened, closed, and routed on demand. In this work, we propose a hexagonal pendant-type acoustic metamaterial (AM) that implements an accidental-Dirac-cone-based independent tuning mechanism in an acoustic system. The designed unit cell contains two types of cylinder-frame connectors with independently adjustable rotational angles, {\theta }_1 and {\theta }_2, which provide two geometric degrees of freedom for modulating the acoustic band structure. Finite element analysis reveals that the pristine structure supports three accidental Dirac cones in low-, mid-, and high-frequency regimes. By rotating the connectors to break mirror symmetry, the degeneracies of these Dirac cones can be selectively lifted or preserved, thus leading to independently tunable acoustic bandgaps and valley topological phases. The topological characteristics are identified through modal analysis, Berry curvature distributions, and valley Chern numbers. Interfaces between domains with opposite valley Chern numbers support topologically protected interface modes in the corresponding frequency intervals. A supercell analysis confirms the existence of single-, dual-, and triple-frequency interface states with pronounced sound-pressure confinement along the interfaces. Based on these states, frequency-selective acoustic waveguides are constructed to realize directional transport, wave separation, and acoustic demultiplexing under single-, dual-, and triple-frequency excitations. The results show that acoustic waves at different frequencies can be routed along prescribed paths with high selectivity and stable transmission in the presence of typical structural defects. The present numerical study therefore provides an acoustic implementation of independently tunable accidental-Dirac-cone-based topological transport and offers a feasible route for integrated acoustic-waveguiding, filtering, and demultiplexing devices.

A compression-torsion combined loading method for soft materials based on metamaterials

Ziji YIN, Lingling HU, Yongrou ZHANG

2026, 47(9):  1901-1918.  doi:10.1007/s10483-026-3430-8

Abstract ( 16 )   PDF (698KB) ( 3 )  

References | Related Articles | Metrics

Soft materials often experience complex multi-axial stress states in practical applications; however, most existing mechanical experimental studies are primarily limited to single-loading mode tests, owing to the technical and cost constraints of combined loading systems. In this paper, we propose a combined loading method for soft materials using a mechanically designed metamaterial. The inherent architecture of the metamaterial converts an input compressive load into a combined compressive-torsional output, enabling combined loading experiments with only a conventional universal testing machine. To match the low stiffness of soft materials, the metamaterial is fabricated from thermoplastic polyurethane and integrated with a metal plate at the specimen contact surface, ensuring visible torsional deformation under low pressure while retaining sufficient load-bearing capacity. Furthermore, when soft materials undergo large deformation, direct surface speckling for digital image correlation (DIC) becomes impractical due to the speckle distortion. To overcome this, a “brim” is incorporated to track the relative displacement between the metamaterial and loading platen, thereby allowing indirect calculation of the overall specimen strain. To ensure efficient torque transmission, the two end faces of the specimen need to be securely bonded. A correction method is also developed to mitigate the stress measurement errors caused by end-face bonding effects. Using silicone as a representative soft material, we validate the proposed approach by characterizing its mechanical response under combined compression-torsion loading and establishing a corresponding viscoelastic constitutive model. The results reveal notable strain-rate dependence and strong nonlinearity in the mechanical behavior of silicone, and suggest that constitutive parameters calibrated solely from uniaxial compression tests may be inadequate for predicting the behavior under complex stress states. The developed experimental technique provides an effective means for advancing the comprehensive mechanical characterization of soft materials under multi-axial loading.

Rayleigh wave manipulation in piezoelectric layered media via rod-type locally resonant metamaterials

Zhiqiang HOU, Aibing ZHANG, Jianke DU, Jia LOU

2026, 47(9):  1919-1942.  doi:10.1007/s10483-026-3432-6

Abstract ( 12 )   PDF (1907KB) ( 2 )  

References | Related Articles | Metrics

A surface acoustic wave (SAW) device, which is indispensable in a modern communication and sensing system, typically has a piezoelectric thin film deposited on an elastic substrate. As the operating frequency increases, the desired mode in such layered structures is increasingly accompanied by the spurious modes, which severely degrade the device performance. Although locally resonant (LR) metamaterials have shown potential for sub-wavelength wave manipulation, their coupling with layer-induced dispersion in piezoelectric layered media remains unexplored. Here, we establish an analytical model to reveal how this coupling governs the bandgap formation. By comparing the high-velocity (AlN-Si) and low-velocity (LiNbO₃-Si) systems, we uncover two distinct mechanisms: the high-velocity system enables a complete bandgap; in the low-velocity system, higher-order modes traverse the resonant frequencies without the classic avoided-crossing behavior, preventing the complete bandgap formation. These findings establish quantitative design guidelines for the selective spurious mode suppression in next-generation SAW devices.

Dynamic modeling and control for flexible bodies with mobile control moment gyroscopes

Zhou YANG, Xinyuan LI, Dongping JIN, Ti CHEN

2026, 47(9):  1943-1968.  doi:10.1007/s10483-026-3431-9

Abstract ( 14 )   PDF (7687KB) ( 3 )  

References | Related Articles | Metrics

This paper investigates the dynamic modeling and vibration suppression of a flexible cantilever body with mobile control moment gyros (CMGs). A nonlinear dynamic model capturing the rigid-flexible coupling between the structure and the mobile CMG is systematically derived by Kane’s method. Vibration suppression is realized via the gyroscopic coupling caused by the direction change of the CMG’s angular momentum. To address the practical challenge of unmeasurable states, a neural network (NN)-based cascaded observer with a super-twisting differentiator is designed for real-time state estimation. A radial basis function (RBF) NN is used to approximate the nonlinear terms and disturbances in the system. Based on the observed states and the NN, a sliding mode controller based on the observer’s estimations is synthesized to achieve simultaneous trajectory tracking of the mobile CMG and active vibration suppression of the flexible structure. Numerical simulations demonstrate the effectiveness of the proposed method. Comparisons between the fixed CMG and mobile CMG are carried out to illustrate the advantages of the CMG acting as a mobile actuator.

Cell-based distributed NiTi-ST damping for dynamic vibration control of hourglass composite lattice sandwich beams

Zhijian WANG, Jian ZANG, Xiaodong LI, Yewei ZHANG, Liqun CHEN

2026, 47(9):  1969-1990.  doi:10.1007/s10483-026-3423-9

Abstract ( 14 )   PDF (8557KB) ( 4 )  

References | Related Articles | Metrics

Hourglass composite lattice sandwich beams (HCLSBs) possess excellent stiffness-to-weight efficiency, yet their dynamic vibration response requires further investigation. This paper establishes a modified Timoshenko beam model with bending-shear coupling for HCLSBs. The vibration response is systematically analyzed by the Galerkin truncation method (GTM) combined with the harmonic balance method (HBM), and the modal characteristics are validated through the finite element analysis and impact hammer experiments on fabricated physical specimens. On this basis, two distributed passive damping schemes based on nitinol steel wire rope (NiTi-ST) are designed and compared, including embedded and cell-based configurations. Vibration experiments demonstrate that both schemes effectively attenuate resonant responses. However, the NiTi-ST cell configuration exhibits superior damping efficiency on a mass-normalized basis. The proposed modeling framework and the distributed damping strategy provide an effective solution for vibration suppression in lightweight lattice structures, holding significant potential for applications in structural dynamics and control engineering, particularly in aerospace component design.

Nonlinear vibrations of variable-thickness titanium laminates reinforced with twisted bilayer graphene

Zuohua FU, Wei ZHANG, Yufei ZHANG

2026, 47(9):  1991-2020.  doi:10.1007/s10483-026-3424-6

Abstract ( 9 )   PDF (19862KB) ( 2 )  

References | Related Articles | Metrics

This study investigates the nonlinear vibration characteristics of functionally-graded twisted bilayer graphene reinforced titanium (FG-TBLG-RT) cantilever trapezoidal laminated plates with variable thickness, targeting lightweight, and vibration-resistant structures for unmanned aerial vehicles (UAVs). A novel mechanical model is developed, aiming at coupling the functionally-graded material (FGM) distributions with a variable-thickness cantilevered trapezoidal geometry so as to represent lightweight UAV wing structures, and a comprehensive theoretical framework is established with the 1st-order shear deformation theory and von Kármán geometric nonlinearity. The governing equations are solved by the Rayleigh-Ritz method, Galerkin method, Runge-Kutta (R-K) method, and harmonic balance method (HBM). The accuracy of the proposed model is successfully validated by both the finite element analysis (FEA) and the experimental tests, demonstrating excellent agreement with a maximum deviation of less than 5%. A systematic analysis is conducted to reveal the effects of the twisted bilayer graphene (TBLG) weight fraction, distribution patterns, and geometric parameters on the natural frequencies. Furthermore, this work explicitly uncovers and experimentally validates the highly complex and pronounced nonlinear behaviors, including 1:1 internal resonance, bifurcation, and chaotic motions, under combined transverse and in-plane excitations. These original findings offer crucial and unprecedented theoretical guidance for the dynamic safety and robust design of low-altitude aerospace structures.

Nonlinear analysis of deformation-polarization-carrier coupling fields in controllable heterogeneous PN junction nanodevices incorporating surface effect

Wenjun WANG, Miaomiao LI, Luke ZHAO, Feng JIN, Tao HOU, Tingting ZHAO, Tianhu HE, Yongbin MA

2026, 47(9):  2021-2042.  doi:10.1007/s10483-026-3428-6

Abstract ( 8 )   PDF (871KB) ( 1 )  

References | Related Articles | Metrics

In this paper, a nonlinear magneto-thermo-mechanical coupling theoretical model related to the coupled extensional and flexural deformation working modes of controllable heterogeneous PN junction devices is established, and the screening effect caused by the doping levels of the initial mobile carrier concentrations, the surface effect and critical thickness of the average electric field, and the active manipulation mechanism and evolution law for the deformation-polarization-carrier coupling fields are investigated. The results show that a relatively moderate doping level can effectively improve the transport behaviors and distribution characteristics of the electrons and holes in the PN junction. When the thickness of the PN junction device is reduced to a critical value, the size-dependent behavior caused by the surface effect owing to the average electric field difference is obvious. The working performance of the controllable giant magnetostrictive Terfenol-D based heterogeneous PN junction device can be improved evidently when the Terfenol-D layers of the laminated nanoplate devive are subjected to the changing operating temperature, applied external magnetic field, or pre-stress stimuli. These findings can provide effective guidance for the explanation of the nonlinear magneto-mechanical-thermo coupling active manipulation mechanism for induced deformation-polarization-carrier coupling fields, as well as the experimental design of Terfenol-D based heterogeneous PN junction nanodevices.

Active quasi-zero stiffness vibration isolator for time-varying load conditions

Tianci JIANG, Guangdong SUI, Wentao WU, Xiaobiao SHAN, M. ELSAMANTY

2026, 47(9):  2043-2062.  doi:10.1007/s10483-026-3429-7

Abstract ( 8 )   PDF (1516KB) ( 2 )  

References | Related Articles | Metrics

To resolve the deteriorated vibration isolation performance of existing passive quasi-zero stiffness (QZS) vibration isolators caused by time-varying loads and stiffness mismatch, this paper proposes a novel load-adaptive QZS vibration isolator (LAQVI) based on radial basis function (RBF) neural network adaptive sliding mode control (SMC). The isolator adopts a composite structure coupling linear springs and electromagnetic units, which delivers adjustable QZS characteristics based on a nonlinear stiffness compensation mechanism. This paper analyzes the influence of various key parameters on the QZS characteristics. Dynamic equation analysis clarifies the relationship between load mismatch and displacement transmissibility, and theoretical studies confirm that excitation current control effectively enhances isolation performance. In addition, a sliding mode controller based on RBF neural network adaptation is designed, leveraging the RBF neural network’s learning and adaptive capabilities for rapid load variation estimation. Simulation results show that the adaptive control of excitation current can effectively compensate for the deviation of the isolation platform and enhance vibration isolation performance. Finally, static experiments verify the QZS characteristics of the isolator, and dynamic load experiments demonstrate the controller’s adaptive adjustment ability for load changes. Vibration test results show that the LAQVI exhibits reliable load adaptability and effective low-frequency vibration isolation performance under time-varying load conditions. The proposed LAQVI provides a theoretical basis for the application of QZS vibration isolators in fields such as intelligent equipment.

Nonlinear dynamic evolution and sensitivity analysis of marine parallel propulsion system: theory and experiment

Jianghai XU, Yudie TAO, Zhongliang XIE, Chunxiao JIAO, Donglin ZOU, Zhushi RAO, Guilin SHE

2026, 47(9):  2063-2088.  doi:10.1007/s10483-026-3427-9

Abstract ( 11 )   PDF (4874KB) ( 1 )  

References | Related Articles | Metrics

The parallel propulsion system is the primary choice for power systems of large-scale ships. However, its operational state is influenced by multiple parameters, and unclear dynamic mechanisms critically restrict its navigation stability and reliability. This study develops a coupled lateral-torsional-longitudinal nonlinear dynamic model to establish the mapping between the key system parameters and the transmission vibration amplitude as well as the gear meshing state. Through the global sensitivity analysis, this study investigates the main effect sensitivity, total effect sensitivity, and interaction effect sensitivity of different parameters on the transmission structure, identifying the dominant factors affecting meshing vibration for different gear pairs. Subsequently, both full-scale ship vibration tests and small-scale prototype experiments are conducted to thoroughly investigate the influence patterns of various parameters on the vibration, acoustic, and power efficiency characteristics of the system. The research results provide essential technical support for a reasonable parameter configuration in such systems and for proactively mitigating the risk of abnormal vibrations.

Multi-material robust topology optimization for high-performance heat exchangers

Zelin WANG, Zhenzhou LU, Yizhou CHEN, Jiangji QU, Xingcheng WANG

2026, 47(9):  2089-2108.  doi:10.1007/s10483-026-3425-7

Abstract ( 14 )   PDF (1817KB) ( 2 )  

References | Related Articles | Metrics

To design an efficient and robust integrated heat exchanger configuration, this work develops a multi-material robust topology optimization (RTO) model, and simultaneously considers the distribution of solid, fluid, and metal foam. In the proposed RTO model, the inlet flow velocity and the metal foam porosity are both treated as random variables, while two pseudo-density fields function as design variables. The objective is to maximize both the heat exchange performance mean and thermal robustness, subject to the constraints that the flow dissipation mean ({\mu }_J) and the structural average strain energy mean ({\mu }_C) are less than their thresholds. To solve the RTO model efficiently, polynomial chaos expansion is adopted to propagate random uncertainties from the input variables to the multi-physical response of the heat exchanger. The two-dimensional (2D) multi-material-based RTO results demonstrate that compared with the deterministic topology optimization (DTO) configuration, when {\mu }_J is constrained to 10 and 20 times that of the straight channel configuration, the heat exchange performance mean of the RTO configuration is improved by 13.85% and 18.01%, and the robustness is improved by 29.54% and 29.65%. Notably, the metal foam in the configuration obtained by the RTO is distributed around the flow channels. For the three-dimensional (3D) multi-material-based RTO, with {\mu }_J and {\mu }_C constrained to 0.8 and 1.2 times the corresponding values of the straight multi-channel configuration, the mean performance and robustness are improved by 33.35%-42.54% and 53.71%-59.88%, respectively. Furthermore, compared with the conventional bi-material RTO method, the 3D heat exchanger configuration obtained by the proposed multi-material RTO method possesses superior heat transfer performance mean and enhanced thermal robustness, while achieving lower flow dissipation and reduced average structural strain energy.

High-order large eddy simulation of incompressible turbulent flow by variational multiscale method

Linfeng CHEN, Xianglu JIA, Peng XU, Yuhong DONG, Jiafeng WU, Chen NIU, Jie ZHU, Fuchang ZHOU

2026, 47(9):  2109-2122.  doi:10.1007/s10483-026-3426-8

Abstract ( 15 )   PDF (488KB) ( 3 )  

References | Related Articles | Metrics

This paper introduces an hp-refinement high-order finite element discretization based on a modified hierarchical Jacobian polynomial basis into a residual-based large eddy simulation (LES) by variational multiscale method (VMM). A high-order finite element basis is achieved by means of p-refinement by introducing a modified hierarchical Jacobian polynomial basis. The benchmark turbulent channel flow is computed using in-house finite element codes with three different orders of the Jacobian polynomial basis. The near-wall flow field and turbulent statistical results obtained using the same degrees of freedom (DOFs) are compared. The results show that the accuracy is significantly improved with the increasing order. The transportation equation of the turbulent kinetic energy is then derived with the VMM, and statistical dissipations are presented to clarify the improvement in the numerical accuracy by high-order simulations. In addition, the matrix structures of linear systems built using different orders of polynomial basis are presented, and the variation in the computational cost with the order of the finite element basis is explained. Furthermore, comparison of the computational costs for cases with equivalently accurate results is made to assess the computational efficiency of the high-order numerical method. Consequently, the results provide compelling evidence for the power of the high-order LES technique with the hp-refinement discretization, which not only reduces the DOFs to be solved, but also achieves the higher computational efficiency than low-order methods.