Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy

Successful application of photonic crystals has led recently to a rapidly growing interest in the analogous acoustic effects in periodic elastic structures called phononic crystals. This study is aimed at developing a theory for two-dimensional phononic crystal consisting of materials with general anisotropy. Explicit formulations of the plane harmonic bulk wave and the surface wave dispersion relations in such a general phononic structure are derived based on the plane wave expansion method. Two-dimensional phononic structures with either the square or the hexagonal lattice are considered in the numerical examples. Band gap characteristics of the phononic structures with different anisotropic background materials (isotropic, cubic, hexagonal, and orthorhombic) are calculated and discussed.