一种局域共振型声学超材料的半解析建模与带隙机制研究

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (3) : 27-36.

论文

赵振成1,2，张涵柯1,2，郑玲1,2

作者信息 +

Semi-analytical modeling and bandgap mechanism of a local resonance type acoustic metamaterial

ZHAO Zhencheng1,2, ZHANG Hanke1,2, ZHENG Ling1,2

Author information +

文章历史 +

摘要

基于声学黑洞（acoustic black hole，ABH）弧形梁体积小且模态频率丰富的特点，将声学黑洞弧形梁作为附加结构周期分布在直梁上，达到促进局域共振效应和拓宽低频带隙的作用，由此构建一种新的局域共振型声学超材料。针对局域共振型超材料，采用高斯展开法，建立其半解析理论分析模型，基于零空间法处理其内部连接以及周期边界条件，并通过有限元法验证半解析理论分析模型的准确性。分析和计算其能带结构，研究结构参数以及ABH效应对布拉格带隙以及局域共振带隙的影响机理。研究结果表明，该半解析理论模型能够对结构的带隙进行有效计算，附加弧形ABH的陷波机制能够促进结构的局域共振效应并对主梁进行有效减振，为声学黑洞声学超材料的应用提供了新的思路。

Abstract

Based on the characteristics of ABH (acoustic black hole) arc beam with small volume and rich modal frequencies, ABH (acoustic black hole) arc beam is periodically distributed on the straight beam as an additional structure and coupled with the straight beam to promote the local resonance effect and broaden the low-frequency band gap, and a new local resonance acoustic metamaterial is constructed. For local resonant metamaterials, the semi analytical theoretical analysis model is established by using the Gaussian expansion method. The internal connection and periodic boundary conditions are treated based on the null space method. The accuracy of the semi analytical theoretical analysis model is verified by the finite element method. The energy band structure is analyzed and calculated, and the influence mechanism of structural parameters and ABH effect on Bragg band gap and local resonance band gap is studied. The results show that the semi analytical theoretical model can effectively calculate the band gap of the structure, and the notch mechanism with arc ABH can promote the local resonance effect of the structure and effectively reduce the vibration of the main beam.

导出引用

赵振成1,2，张涵柯1,2，郑玲1,2. 一种局域共振型声学超材料的半解析建模与带隙机制研究[J]. 振动与冲击, 2024, 43(3): 27-36

ZHAO Zhencheng1,2, ZHANG Hanke1,2, ZHENG Ling1,2. Semi-analytical modeling and bandgap mechanism of a local resonance type acoustic metamaterial[J]. Journal of Vibration and Shock, 2024, 43(3): 27-36

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