多稳态粘弹性超材料及其可调带隙特性研究

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

摘要/Abstract

摘要： 源于独特的带隙特性，超材料因良好的减振能力而受到广泛关注。本文设计了一种新型多稳态粘弹性超材料构型，通过调节外部加载速率控制形变。基于3D打印技术制备了试件，单轴压缩试验表明该超材料单胞具有显著的双稳态形变特性。研究了该多稳态粘弹性超材料可调的带隙特性和有限周期振动传递特性，并与其未变形构型进行了对比分析。计算结果表明，与未变形结构相比，形变可显著拓宽多稳态粘弹性超材料0~300 Hz的多条带隙；在相同压缩量下，多稳态粘弹性超材料的抑振特性还可通过调节外部加载速率进行改变；准静态加载工况下，多稳态粘弹性超材料可对50 Hz以下振动实现有效抑制。本文的超材料对动态加载具有显著的粘滞效应特性，与单稳态超材料相比，具有更多样化的带隙调节能力。

关键词: 粘弹性超材料; 多稳态结构; 色散关系; 带隙特性; 有限元法

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

中图分类号:

TB34

孟永毅, 曹勇, 薛彦平, 刘利平, 杨冬, 刘永文, 折强, 田永雄, 刘小智. 多稳态粘弹性超材料及其可调带隙特性研究[J]. 人工晶体学报, 2026, 55(5): 801-808.

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.

图/表 9

图1 粘弹性超材料几何构型

Fig.1 Geometrical configuration of viscoelastic metamaterial

表1 模型材料参数［15?16］

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

图2 粘弹性超材料有限元建模

Fig.2 Finite element modelling of viscoelastic metamaterial

表2 粘弹性材料（Agilus）Prony系数［15］

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

图3 粘弹性超材料应力-应变关系及其中点挠度

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

图4 粘弹性超材料实验件及不同速率下的构型变化对比

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

图5 粘弹性超材料形变元胞（a）~（c）及色散关系（d）~（f）

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

图6 粘弹性超材料低频带隙变化曲线

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

图7 有限周期超材料传输曲线及对应振型

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

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