基于Peano分形的亚波长尺度声学超材料

吴光华,柯艺波,张林,陶猛

振动与冲击 ›› 2022, Vol. 41 ›› Issue (23) : 241-248.

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PDF(3473 KB)
振动与冲击 ›› 2022, Vol. 41 ›› Issue (23) : 241-248.
论文

基于Peano分形的亚波长尺度声学超材料

  • 吴光华,柯艺波,张林,陶猛
作者信息 +

Sub-wavelength scale acoustic metamaterial based on Peano fractal

  • WU Guanghua,  KE Yi-bo, ZHANG Lin, TAO Meng
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文章历史 +

摘要

基于Peano分形曲线设计了亚波长尺度的二维分形结构,该结构在特定频率范围内具有负质量密度和负体积模量,利用S参数法和传递矩阵的方法计算出等效质量密度和等效体积模量。基于有限元方法研究了分形结构在特定频率范围内声波的调控特性如近零密度传输、声隐身、声隧穿和波前整形等,分析了这些声特性与分形结构透射系数峰值频率的对应关系。基于3D打印技术制作了分形结构样品,实测的透射系数与计算分析结果有很好的一致性,说明了分析方法的有效性。结果表明,设计出的超材料有着特殊的声学参数,在[0, 1600]Hz内有多条带隙,可以用于低频下的滤波和声调控。
关键词:分形结构;声调控;带隙特性;近零密度传输;声隐身

Abstract

Inspired by Peano fractal curves, a new type of two-dimensional fractal structure on the sub-wavelength scale is constructed, which has negative mass density and bulk modulus in specific frequency ranges. The S-parameter method and transfer matrix method are used for calculating effective mass density and bulk modulus. Based on the finite element method, the sound modulation characteristics of the fractal structure in specific frequency ranges are studied, such as density-near-zero transmission, acoustic cloaking, sound tunneling, and wavefront shaping. The corresponding relationship between the acoustic characteristics and the frequency of peak transmission coefficient for fractal structure is analyzed. Based on the 3D printing technology, the structure sample is fabricated. The transmission coefficient measured by the experiment is in good agreement with the calculated results, which shows the effectiveness of the analysis method. The results show that the designed metamaterial has novel acoustic parameters and multiple band gaps within [0, 1600] Hz, which can be used for filtering and sound modulation at the low-frequency band.
Key words: Fractal structure; Sound modulation; Bandgap; Density-near-zero transmission; Acoustic cloaking

关键词

分形结构 / 声调控 / 带隙特性 / 近零密度传输 / 声隐身

Key words

Fractal structure / Sound modulation / Bandgap / Density-near-zero transmission / Acoustic cloaking

引用本文

导出引用
吴光华,柯艺波,张林,陶猛. 基于Peano分形的亚波长尺度声学超材料[J]. 振动与冲击, 2022, 41(23): 241-248
WU Guanghua, KE Yi-bo, ZHANG Lin, TAO Meng. Sub-wavelength scale acoustic metamaterial based on Peano fractal[J]. Journal of Vibration and Shock, 2022, 41(23): 241-248

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