The transmission properties of elastic waves through multilayers of spheres with planar defects

Abstract

The work presented in this paper discusses the transmission properties of elastic waves through multilayers of spheres which are periodically arranged in a homogeneous host material. The multilayers of spheres can have different kinds of planar defects. These defects are formed by removing one layer of spheres or by changing the radiuses or the material of scatterers in some layers. First, the reflection and transmission matrices of a single layer of spheres are obtained by the multiple scattering approaches and then the reflection and transmission matrices of multilayers of spheres are derived based on the polymerization method. Numerical examples are presented for 15 layers of spheres with one central planar defect layer or two symmetrically arranged planar defect layers. The influences of these planar defects on the frequency-dependent transmission curves are discussed. It is observed that the band gap can be widened evidently by introducing the planar defect, and the defect states appear in the band gap consequently. So the elaborately arranged planar defects are important in designing specific acoustic filters.