Effects of material parameters on the band gaps of two-dimensional three-component phononic crystals

In this paper, the effects of material parameters on the band gaps of two-dimensional (2D) three-component phononic crystals (PCs) are investigated based on improved plane wave expansion method (IPWE). The theoretical derivation is based on the elastic wave equations, and the effects on band gaps for both in-plane (xy-mode) and anti-plane modes (z-mode) are discussed in detail. Results show that the material parameters directly determining the band gaps include mass density ratio, shear modulus ratio, and Poisson’s ratio for xy-mode, and mass density ratio and shear modulus ratio for z-mode; for the three-component PCs with Bragg gaps, wide band gap appears in the case of large density mismatches and large shear modulus ratio of scatterer to matrix, and the Poisson’s ratio of the matrix has more influence on the band gap; for the three-component PCs with local resonance gaps, wide band gap appears in the case of large mass density ratio of scatterer to matrix and small mass density ratio of coating layer to matrix, large shear modulus ratio of scatterer to matrix and small shear modulus ratio of coating layer to matrix. These conclusions can be used to guide the band gap designing of the three-component PCs.