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

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

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。

Based on small volume and rich modal frequencies of acoustic black hole(ABH)arc beam,ABH arc beams as additional structures are periodically distributed on a straight beam to promote local resonance effect,broaden low-frequency bandgap,and construct a new local resonance type acoustic metamaterial.Here,for a local resonance type metamaterial,Gaussian expansion method was used to establish its semi-analytical theoretical analysis model.Its internal connections and periodic boundary conditions were processed using the zero-space method,and the correctness of the semi-analytical theoretical analysis model was verified with finite element method.Its energy band structure was analyzed and calculated to study the influence mechanism of structural parameters and ABH effect on Bragg bandgap and local resonance bandgap.The study results showed that the established semi-analytical theoretical model can effectively calculate structure bandgap;the notch mechanism of additional arc-shaped ABH can promote the structure’s local resonance effect and effectively reduce vibration of main beam;the study results can provide new ideas for application of ABH acoustic metamaterials.