Multi-Stable Viscoelastic Metamaterials and Their Tunable Bandgap Properties

doi:10.16553/j.cnki.issn1000-985x.2025.0244

Abstract

Abstract: Metamaterials， characterized by their unique bandgap properties， have garnered significant attention for their exceptional ability to attenuate vibrations. In this study， a novel multi-stable viscoelastic metamaterial configuration was designed， with its deformation controlled by adjusting the external loading rate. Specimen was fabricated using 3D printing technology， and uniaxial compression tests demonstrate that the unit cell of this metamaterial exhibits significant bistable deformation characteristics. The tunable bandgap characteristics and finite-period vibration transmission characteristics of this multi-stable viscoelastic metamaterial were investigated， and a comparative analysis was conducted with its undeformed configuration. The simulation results indicate that， compared to the undeformed case， structural deformation can significantly broaden multiple bandgaps of the multi-stable viscoelastic metamaterial within the 0~300 Hz range. Under the same compression level， the vibration suppression properties of the multi-stable viscoelastic metamaterial can also be altered by adjusting the external loading rate. Under quasi-static loading conditions， the multi-stable viscoelastic metamaterial can effectively suppress vibrations below 50 Hz. The proposed metamaterial exhibits significant viscous effects under dynamic loading， and compared to single-stable metamaterials， possesses more diverse bandgap tuning capabilities.

Key words: viscoelastic metamaterial; multi-stable structure; dispersion relation; bandgap characteristic; finite element method

CLC Number:

TB34

MENG Yongyi, CAO Yong, XUE Yanping, LIU Liping, YANG Dong, LIU Yongwen, ZHE Qiang, TIAN Yongxiong, LIU Xiaozhi. Multi-Stable Viscoelastic Metamaterials and Their Tunable Bandgap Properties[J]. Journal of Synthetic Crystals, 2026, 55(5): 801-808.

Figures/Tables 9

Fig.1 Geometrical configuration of viscoelastic metamaterial

Table 1 Material parameter for model［15?16］

Parameter	PETG	Hei-Cast	Agilus
G/（10⁶ N·m²）	1.44	0.430	0.286
ρ/（kg·m^-3）	1 270	1 200	1 300

Fig.2 Finite element modelling of viscoelastic metamaterial

Table 2 Prony series coefficients for viscoelastic material （Agilus）［15］

Serial number	g	τ
1	0.017 279	8.699 4
2	0.694 38	0.240 26
3	0.048 5	557.714 7
4	0.017 237	8.701 3
5	0.017 239	8.696 7
6	0.017 183	8.706 4
7	0.017 551	8.699 1

Fig.3 Stress-strain relationship and mid-point deflection of viscoelastic metamaterial

Fig.4 Viscoelastic metamaterial specimen and its configuration changes at different rates

Fig.5 Deformed unit cells （a）~（c） and dispersion relations （d）~（f） of viscoelastic metamaterial

Fig.6 Variation curves of low-frequency bandgaps of viscoelastic metamaterial

Fig.7 Transmission curves and corresponding mode shapes of finite-period metamaterials

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