Bandgap Regulation Characteristics of Multi-Stable Metamaterial with Flexural Elastic Beams Structure

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

Abstract

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

CLC Number:

O328

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.

Figures/Tables 13

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

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

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

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

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

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

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

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

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

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

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

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

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

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