Band structures of metacomposite based phononic crystals in quasi-Sierpinski fractals

Abstract

In this paper, we investigated the bandgaps of two-dimensional phononic crystals with quasiSierpinski carpet unit cells in a metacomposite based solid–solid phononic crystal. Finite element method was used to analyze the properties of two-dimensional phononic bandgaps (2D PBGs) in a quasi-fractal structure. Two new types of quasi-Sierpinski fractal unit cells whose constituents are homogeneous and isotropic were proposed to obtain larger full bandgaps. The results show that the PBGs of the proposed quasi-Sierpinski fractals are suitable to tune the PBG’s without changing the size of the phonic crystal. The new quasi-Sierpinski fractals also retain the selfsimilarity as in the third-order Sierpinski fractal unit cell. The investigated quasi-fractals can be easily modified to increase the filling fraction of the constituents, which can be effectively used to enlarge existing PBG by preserving degree of self-similarity structure.