Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals

摘要

In this paper we study the influences of the material parameters on phononic band gaps of two-dimensional solid phononic crystals. The analysis begins with the basic wave equations and derives the material parameters directly determining band gaps. These parameters include the mass density ratio, the shear modulus ratio, and Poisson's ratios of the scatterer and host materials (or equivalently, the wave velocity ratio, the acoustic impedance ratio, and Poisson's ratios). The effects of these parameters on phononic band gaps are discussed in details for phononic crystals with different filling fractions and lattice forms for both antiplane and in-plane wave modes. Band gaps are calculated by the plane wave expansion method. The results show that for the antiplane mode, the mass density ratio predominantly determines the band gap, while that for the in-plane mode, both mass density ratio and shear modulus ratio play equally important roles. The maximum band gap will appear at both large density ratio and shear modulus ratio (i.e., large acoustic impedance ratio with small mismatch in wave velocities) for either antiplane or in-plane wave mode; but band gaps may 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 artificial design of band gaps.