Abstract We constructed a three-dimensional fractal acoustic metamaterial using the combination of zigzag channels and Menger fractal structures that had high structural symmetry and could extend into 3D space easily. Reflection and transmission coefficients were numerically calculated and experimentally measured, and the results matched well with each other. Using the finite element method and the S-parameter retrieval method, the band structures, the equivalent frequency surface and the effective parameters of the acoustic metamaterial were calculated. The results showed that the 3D acoustic metamaterial had double negative property in the normalized frequency range of 0.205–0.269 and density-near-zero property in the normalized frequency vicinity of 0.356. A plate lens model and a quarter-bending model were constructed to demonstrate the double negative property and the density-near-zero property of the acoustic metamaterial, respectively. These results showed that the 3D acoustic metamaterial could achieve excellent acoustic properties and would be promising to construct the 3D double negative structure and control acoustic waves on a subwavelength scale within a single unit.

中文翻译：

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亚波长尺度上具有双负和密度近零特性的三维分形结构

摘要 我们利用锯齿形通道和门格尔分形结构的组合构建了一种具有高度结构对称性且易于扩展到3D空间的三维分形声学超材料。反射系数和透射系数进行了数值计算和实验测量，结果相互吻合。利用有限元法和S参数反演法计算了声学超材料的能带结构、等效频率面和有效参数。结果表明，3D 声学超材料在 0.205-0.269 的归一化频率范围内具有双重负特性，在 0.356 的归一化频率附近具有密度接近零的特性。构建了板透镜模型和四分之一弯曲模型，分别展示了声学超材料的双负特性和密度接近于零的特性。这些结果表明，3D 声学超材料可以实现优异的声学特性，并有望在单个单元内构建 3D 双负结构和控制亚波长尺度的声波。