Elastic band gaps of two-dimensional phononic crystals tunned by material parameters

In this paper, the analysis begins with the basic wave equations and derives the material parameters directly determining band gaps of the mixed in-plane wave mode in a two-dimensional phononic crystal. These parameters include the mass density ratio, the shear modulus ratio and Poisson's ratios of the scatterer and host materials. The effects of these parameters on the band gaps are discussed for different filling fractions and lattice forms. Band gaps are calculated by the plane wave expansion method. The results show that the maximum band gap will appear at both large density ratio and shear modulus ratio; but band gaps may also appear in other situations depending on the filling fraction and lattice forms. It is also shown that neither acoustic impedance ratio nor wave velocity ratio can determine the band gap independently. The present analysis can be applied to artificially design band gaps.