Large band gaps in two-dimensional phononic crystals with self-similarity structure

In this paper, we study the band gaps (BGs) of two-dimensional (2D) phononic crystals (PCs) composed of self-similarity shape inclusions embedded in the homogenous matrix. The dispersion relations, transmission spectra, and displacement fields of eigen-modes of the proposed structures are calculated by use of finite element method. Due to the simultaneous mechanisms of the Bragg scattering, the structure can exhibit low-frequency BGs, which can be effectively shifted by changing the geometries and degree of the self-similarity structure. The BGs are significantly dependent upon the geometrical parameters and degree of the self-similarity structure. It is concluded that, the PCs with self-similarity structure, can modulate the location and width of BGs. But it must be pointed out, the shape of self-similarity inclusion exercises a great influence on the BGs. The study in this paper is relevant to the design of tuning BGs and isolators in the low-frequency range.