弯曲弹性梁多稳态超材料带隙调控特性研究

doi:10.16553/j.cnki.issn1000-985x.2024.0313

摘要/Abstract

摘要： 多稳态超材料能够在外部力作用下发生变形，从而实现对弹性波传播的灵活调控。本文基于双稳态弯曲弹性梁结构，提出了两种不同维度弯曲弹性梁多稳态超材料，该超材料具有两种稳定构型，并能够通过外部力的作用在这两种稳定状态之间切换。通过有限元方法，系统研究了多稳态超材料在两种稳定构型下的色散关系和频率响应特性。研究结果表明，通过调节外部施加的力，可以实现稳态结构的形变，从而有效地调整带隙的频率范围和宽度。此外，将一维多稳态超材料拓展为三维多稳态超材料，可以获得更宽的第一带隙。这种稳态变化机制不仅为弹性波的传播提供了多样化的调控手段，也为弹性波导开关的设计与应用提供了新的思路。

关键词: 多稳态超材料; 带隙; 弯曲弹性梁; 有限元; 减振; 弹性波导开关

Abstract: Multi-stable metamaterial can deform under external forces， enabling flexible manipulation of elastic wave propagation. This paper proposed two multi-stable metamaterials based on the bistable flexural elastic beam structure， with different bending dimensions. These metamaterials possess two stable configurations and can switch between these states under the external forces. The dispersion relation and frequency response characteristics of the multi-stable metamaterial in the two stable configurations were investigated by the finite element method. The results reveal that by adjusting the external applied forces， the stable structure can be deformed， effectively tuning the frequency range and bandwidth of the bandgap. A wider first bandgap range can be obtained by expanding one-dimensional multi-stable metamaterial into three-dimensional multi-stable metamaterial. This shape-changing mechanism not only provides diverse control methods for elastic wave propagation but also offers new insights into the design and application of elastic waveguide switch.

Key words: multi-stable metamaterial; bandgap; bending elastic beam; finite element; vibration reduction; elastic waveguide switch

中图分类号:

O328

魏玉华, 陈新华, 蒋帅, 李小双, 王建广. 弯曲弹性梁多稳态超材料带隙调控特性研究[J]. 人工晶体学报, 2025, 54(5): 832-840.

WEI Yuhua, CHEN Xinhua, JIANG Shuai, LI Xiaoshuang, WANG Jianguang. Bandgap Regulation Characteristics of Multi-Stable Metamaterial with Flexural Elastic Beams Structure[J]. Journal of Synthetic Crystals, 2025, 54(5): 832-840.

图/表 13

图1 一维多稳态超材料单胞

Fig.1 One-dimensional multi-stable metamaterial unit cell

表1 超材料的几何参数

Table 1 Geometric parameters of metamaterial

Parameter	a	d	L	t	b	l
Value/mm	174.7	8.0	123.6	1.0	13.9	25.0

图2 一维多稳态超材料的拉伸稳态与压缩稳态

Fig.2 One-dimensional multi-stable metamaterial in tensile stable state and compressive stable state

图3 三维多稳态超材料单胞的拉伸稳态与压缩稳态

Fig.3 Three-dimensional multi-stable metamaterial unit cell in tensile stable state and compressive stable state

图4 三维结构不可约布里渊区

Fig.4 Irreducible Brillouin Zones of the three-dimensional structure

图5 能带结构分析。（a）拉伸稳态结构的面内能带；（b）压缩稳态结构面内能带结构

Fig.5 Energy band structure analysis. （a） In-plane band structure of the tensile stable state；（b） in-plane band structure of the compressive stable state

表2 带隙范围

Table 2 Bandgap range

Parameter	Energy band structure		Frequency response
Parameter	Tensile stable state	Compressive stable state	Tensile stable state	Compressive stable state
First bandgap range/Hz	51.42~72.53	56.17~81.53	54.5~74.1	57.7~82.5
Second bandgap range/Hz	84.82~89.59	93.14~101.07	85.6~91.3	88.5~98.1
Third bandgap range/Hz	118.85~174.69	113.51~204.07	118.9~177.3	105.3~198.1
Fourth bandgap range/Hz	188.09~192.56	204.59~229.19	190.1~195.7	200.1~224.5

图6 拉伸稳态和压缩稳态第一带隙边缘频率对应的模态

Fig.6 Modes corresponding to edge frequencies of the first bandgap in the tensile stable state and compressive stable state

图7 频率响应分析。（a）频率响应计算模型；（b）拉伸稳态下的频率响应曲线；（c）压缩稳态下的频率响应曲线

Fig.7 Frequency response analysis. （a） Frequency response calculation model；（b） frequency response curve in the tensile stable state；（c） frequency response curve in the compressive stable state

图8 拉伸稳态与压缩稳态第三带隙水平色散曲线对应的模态

Fig.8 Modes corresponding to the horizontal dispersion curve of the third bandgap in the tensile stable state and compressive stable state

图9 能带结构分析。（a）三维拉伸稳态的面内能带；（b）三维压缩稳态的面内能带

Fig.9 Energy band structure analysis. （a）In-plane band structure of the three-dimensional tensile stable state；（b）in-plane band structure of the three-dimensional compressive stable state

图10 三维拉伸稳态和三维压缩稳态超材料频率响应分析

Fig.10 Frequency response analysis of three-dimensional tensile stable and three-dimensional compressive stable metamaterial

图11 三维拉伸稳态与三维压缩稳态的频率响应计算

Fig.11 Frequency response calculation of three-dimensional tensile stable state and three-dimensional compressive stable state

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