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 eigenmodes 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 lowfrequency 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.