Elastic wave scattering by periodic structures of spherical objects: Theory and experiment

We extend the multiple-scattering theory for elastic waves by taking into a ccount the full vector character. The formalism for both the band structure calculation and the reflection and transmission calculations for finite sl abs is presented. The latter is based on a double-layer scheme which obtain s the reflection and transmission matrix elements for the multilayer slab f rom those of a single layer. As a demonstration of applications of the form alism, we calculate the band structures of elastic waves propagating in a t hree-dimensional periodic arrangement of spherical particles and voids, as well as the transmission coefficients through finite slabs. In contrast wit h the plane-wave method, the multiple-scattering approach exhibits advantag es in handling specialized geometries (spherical geometry in the present ca se). We also present a comparison between theory and ultrasound experiment for a hexagonal-close-packed array of steel balls immersed in water. Excell ent agreement is obtained.