Near-zero density fractal acoustic metamaterials for acoustic modulation

High-performance acoustic wave modulation has been an important goal of acoustic research. At present, multifunctional acoustic metamaterials with stable acoustic wave modulation and a single structure are still lacking. In this paper, we introduce the fractal self-similarity principle and design a two-dimensional fractal acoustic metamaterial with sub-wavelength scale by combining the concept of spatial curvature. The band structure of the fractal acoustic metamaterial is firstly numerically calculated, and its band gap formation mechanism is explained from the perspective of modal analysis. Then, the equivalent acoustic parameters of the fractal acoustic metamaterials were obtained by inversion using the equivalent parameter method. The results show that the first- and second-order fractal structures exhibit excellent near-zero density properties near 1456 Hz and 884 Hz, respectively. Subsequently, the acoustic modulation properties of fractal acoustic metamaterials, including wavefront shaping, acoustic stealth, multichannel acoustic transmission, and acoustic demultiplexer, are studied in depth. Finally, samples of the fractal acoustic metamaterial structure were fabricated based on 3D printing technology, and the transmission coefficients of the samples were experimentally tested. The results show that the experimental results are in good agreement with the numerical calculations, proving the accuracy of the calculations and the validity of the structure, and indicating that the proposed fractal acoustic metamaterials can be applied to acoustic wave modulation.