Multistable locally resonant elastic metamaterial with tunable anisotropy

doi:10.1007/s10483-025-3289-8

Abstract

Abstract:

Metamaterials with multistability have attracted much attention due to their extraordinary physical properties. In this paper, we report a novel multistable strategy that is reversible under external forces, based on the fact that a variational reversible locally resonant elastic metamaterial (LREM) with four configurations is proposed. Through a combination of theoretical analysis and numerical simulations, this newly designed metamaterial is proven to exhibit different bandgap ranges and vibration attenuation properties in each configuration. Especially, there is tunable anisotropy shown in these configurations, which enables the bandgaps in two directions to be separated or overlapped. A model with a bandgap shifting ratio (BSR) of 100% and an overlap ratio of 25% is set to validate the multistable strategy feasibility. The proposed design strategy demonstrates significant potentials for applications in versatile scenarios.

Key words: locally resonant metamaterial, multistable, anisotropy, tunable bandgap

2010 MSC Number:

O343

Siyu REN, Yijun CHAI, Xiongwei YANG. Multistable locally resonant elastic metamaterial with tunable anisotropy. Applied Mathematics and Mechanics (English Edition), 2025, 46(9): 1663-1678.

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Figures/Tables 13

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References 40

[1]	GAO, N. S., HOU, H., WU, J. H., and CHENG, B. Z. Low frequency band gaps below 10 Hz in radial flexible elastic metamaterial plate. Journal of Physics D: Applied Physics, 49(43), 435501 (2016)
[2]	CHEN, C., LEI, J. C., and LIU, Z. S. A ternary seismic metamaterial for low frequency vibration attenuation. Materials, 15(3), 1246 (2022)
[3]	YANG, F., MA, Z. Y., and GUO, X. M. Bandgap characteristics of the two-dimensional missing rib lattice structure. Applied Mathematics and Mechanics (English Edition), 43(11), 1631–1640 (2022) https://doi.org/10.1007/s10483-022-2923-6
[4]	CAI, X. B., XIAO, J. F., ZHANG, H. K., ZHANG, Y., HU, G. K., and YANG, J. Compact acoustic double negative metamaterial based on coexisting local resonances. Applied Physics Letters, 113(24), 244101 (2018)
[5]	XIA, B. Z., CHEN, N., XIE, L. X., QIN, Y., and YU, D. J. Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus. Applied Acoustics, 112, 1–9 (2016)
[6]	HUANG, H. H. and SUN, C. T. Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus. Journal of the Mechanics and Physics of Solids, 59(10), 2070–2081 (2011)
[7]	ZHANG, Q. and SUN, Y. X. Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio. Applied Mathematics and Mechanics (English Edition), 44(9), 1457–1486 (2023) https://doi.org/10.1007/s10483-023-3024-6
[8]	WANG, Q., MIAO, L. C., ZHENG, H. Z., XIAO, P., and ZHANG, B. B. Design of elastic metamaterial plate and application in subway vibration isolation. Applied Physics A, 130(8), 557 (2024)
[9]	LU, Z. Q., ZHAO, L., DING, H., and CHEN, L. Q. A dual-functional metamaterial for integrated vibration isolation and energy harvesting. Journal of Sound and Vibration, 509, 116251 (2021)
[10]	CHEN, D. K., ZI, H., LI, Y. G., and LI, X. Y. Low frequency ship vibration isolation using the band gap concept of sandwich plate-type elastic metastructures. Ocean Engineering, 235, 109460 (2021)
[11]	YANG, M., ZHANG, S. L., DING, Y., and FU, Z. J. A combined seismic metamaterial in layered soils. Applied Physics A, 130(8), 586 (2024)
[12]	ZENG, Y., CAO, L. Y., WAN, S., GUO, T., WANG, Y. F., DU, Q. J., ASSOUAR, B., and WANG, Y. S. Seismic metamaterials: generating low-frequency bandgaps induced by inertial amplification. International Journal of Mechanical Sciences, 221, 107224 (2022)
[13]	KIM, E., ZHANG, X. Y., FERREIRA, V. S., BANKER, J., IVERSON, J. K., SIPAHIGIL, A., BELLO, M., GONZÁLEZ-TUDELA, A., MIRHOSSEINI, M., and PAINTER, O. Quantum electrodynamics in a topological waveguide. Physical Review X, 11(1), 011015 (2021)
[14]	DE MELO FILHO, N. G. R., VAN BELLE, L., CLAEYS, C., DECKERS, E., and DESMET, W. Dynamic mass based sound transmission loss prediction of vibro-acoustic metamaterial double panels applied to the mass-air-mass resonance. Journal of Sound and Vibration, 442, 28–44 (2019)
[15]	GAO, N. S. and ZHANG, Z. C. Optimization design and experimental verification of composite absorber with broadband and high efficiency sound absorption. Applied Acoustics, 183(6), 108288 (2021)
[16]	BAO, Y., WEI, Z., JIA, Z., WANG, D., ZHANG, X., and KANG, Z. Mechanical metamaterial design with the customized low-frequency bandgap and negative Poisson's ratio via topology optimization. Extreme Mechanics Letters, 67, 102124 (2024)
[17]	MENG, Z. Q., LIU, M. C., YAN, H. J., GENIN, G. M., and CHEN, C. Q. Deployable mechanical metamaterials with multistep programmable transformation. Science Advances, 8(23), eabn5460 (2022)
[18]	QIAN, W., YU, Z. Y., WANG, X. L., LAI, Y., and YELLEN, B. B. Elastic metamaterial beam with remotely tunable stiffness. Journal of Applied Physics, 119(5), 055102 (2016)
[19]	ZHU, R., CHEN, Y. Y., BARNHART, M. V., HU, G. K., SUN, C. T., and HUANG, G. L. Experimental study of an adaptive elastic metamaterial controlled by electric circuits. Applied Physics Letters, 108(1), 011905 (2016)
[20]	WANG, T., CHAI, Y., GENG, Q., YANG, X., and LI, Y. Tuning characteristics of bandgaps of a mechanical-piezoelectric hybrid elastic metamaterial beam (in Chinese). Chinese Journal of Solid Mechanics, 43(4), 406–418 (2022)
[21]	JIANG, T. X. and HE, Q. B. Dual-directionally tunable metamaterial for low-frequency vibration isolation. Applied Physics Letters, 110(2), 021907 (2017)
[22]	LE, D. H. and LIM, S. Four-mode programmable metamaterial using ternary foldable origami. ACS Applied Materials & Interfaces, 11(31), 28554–28561 (2019)
[23]	PAN, F., LI, Y. L., LI, Z. Y., YANG, J. L., LIU, B., and CHEN, Y. L. 3D pixel mechanical metamaterials. Advanced Materials, 31(25), e1900548 (2019)
[24]	SHI, J. H., MOFATTEH, H., MIRABOLGHASEMI, A., DESHARNAIS, G., and AKBARZADEH, A. Programmable multistable perforated shellular. Advanced Materials, 33(42), e2102423 (2021)
[25]	YIN, C., GENG, Y. H., SHEN, X., YANG, Y., FAN, S. Y., and WANG, T. X. Bandgap variation of a locally resonant metamaterial induced by temperature variation and pre-tension in the shape memory alloy resonators. Smart Materials and Structures, 31(5), 055012 (2022)
[26]	WANG, Z. Y., MA, Z. Y., GUO, X. M., and ZHANG, D. S. A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation. Applied Mathematics and Mechanics (English Edition), 42(11), 1543–1554 (2021) https://doi.org/10.1007/s10483-021-2787-8
[27]	LI, B., ZHANG, C., PENG, F., WANG, W. Z., VOGT, B. D., and TAN, K. T. 4D printed shape memory metamaterial for vibration bandgap switching and active elastic-wave guiding. Journal of Materials Chemistry C, 9(4), 1164–1173 (2021)
[28]	TAO, R., XI, L., WU, W. W., LI, Y., LIAO, B. B., LIU, L. W., LENG, J. S., and FANG, D. N. 4D printed multi-stable metamaterials with mechanically tunable performance. Composite Structures, 252, 112663 (2020)
[29]	GAO, S. S., LIU, W. D., ZHANG, L. C., and GAIN, A. K. A new polymer-based mechanical metamaterial with tailorable large negative Poisson's ratios. Polymers (Basel), 12(7), 1492 (2020)
[30]	ZHOU, X. L., LIU, H. P., ZHANG, J. F., REN, L., ZHANG, L., LIU, Q. P., LI, B. Q., XU, C., and REN, L. Q. 4D printed bio-inspired polygonal metamaterials with tunable mechanical properties. Thin-Walled Structures, 205, 112609 (2024)
[31]	MIZZI, L., HOSEINI, S. F., FORMIGHIERI, M., and SPAGGIARI, A. Development and prototyping of SMA-metamaterial biaxial composite actuators. Smart Materials and Structures, 32(3), 035027 (2023)
[32]	XIANG, J., CHEN, J., ZHENG, Y., LI, P., HUANG, J., and CHEN, Z. Topological design for isotropic metamaterials using anisotropic material microstructures. Engineering Analysis with Boundary Elements, 162, 28–44 (2024)
[33]	YANG, X., CHAI, Y., and LI, Y. Metamaterial with anisotropic mass density for full mode-converting transmission of elastic waves in the ultralow frequency range. AIP Advances, 11(12), 125205 (2021)
[34]	SCHIAVONE, A. and WANG, X. Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation. Wave Motion, 132, 103432 (2025)
[35]	CAI, Y., WU, J. H., XU, Y., and MA, F. Realizing polarization band gaps and fluid-like elasticity by thin-plate elastic metamaterials. Composite Structures, 262, 113351 (2021)
[36]	ZHANG, M., YANG, J., and ZHU, R. Origami-based bistable metastructures for low-frequency vibration control. Journal of Applied Mechanics, 88(5), 051009 (2021)
[37]	JIANG, T., HAN, Q., and LI, C. Topologically tunable local-resonant origami metamaterials for wave transmission and impact mitigation. Journal of Sound and Vibration, 548, 117548 (2023)
[38]	HAN, H., SOROKIN, V., TANG, L., and CAO, D. Origami-based tunable mechanical memory metamaterial for vibration attenuation. Mechanical Systems and Signal Processing, 188, 110033 (2023)
[39]	WU, L. and PASINI, D. In situ switchable local resonance in elastic metamaterials through bistable topological transformation. Applied Physics Letters, 122(22), 221702 (2023)
[40]	DENG, Z., LI, Y., and GAO, G. Bandgap tunability and programmability of four-leaf clover shaped elastic metastructures. Thin-Walled Structures, 200, 111965 (2024)