基于Peano分形的亚波长尺度声学超材料

Sub-wavelength scale acoustic metamaterial based on Peano fractal

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[0,1 600]Hz内有多条带隙,可以用于低频下的滤波和声调控。

Here, based on Peano fractal curve, a 2 D fractal structure with sub-wavelength scale was designed, itcould have negative mass density and negative bulk modulus within a specific frequency range. S-parameter method and transfer matrix method were used to calculate equivalent mass density and equivalent bulk modulus.Based on the finite element method, acoustic control characteristics of fractal structure within a specific frequency range, such as, near-zero density transmission, acoustic stealth, acoustic tunneling and wavefront shaping were studied. The corresponding relations between these acoustic characteristics and peak frequency of transmission coefficient of fractal structure were analyzed. The fractal structure specimens were made based on 3 D printing technology. The actually measured transmission coefficient agreed well with the calculation analysis results to verify the effectiveness of analysis method.The results showed that the designed metamaterial can have special acoustic parameters, multi-band gap within the frequency range of 0-1 600 Hz, and be used for filtering and soundcontrolunder low frequencies.