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

TLDR

The study extends multiple‑scattering theory for elastic waves to a fully vectorial formulation and applies it to compute band structures and transmission through periodic spherical particle arrays. The authors develop a vector‑elastic multiple‑scattering formalism, deriving band‑structure equations and a double‑layer scheme for slab reflection/transmission matrices, and apply it to 3‑D periodic spherical particle arrays and a hexagonal‑close‑packed steel‑ball water array. The vector multiple‑scattering method outperforms plane‑wave approaches for spherical geometries and matches experimental ultrasound data for a hexagonal‑close‑packed steel‑ball array.

Abstract

We extend the multiple-scattering theory for elastic waves by taking into account the full vector character. The formalism for both the band structure calculation and the reflection and transmission calculations for finite slabs is presented. The latter is based on a double-layer scheme which obtains the reflection and transmission matrix elements for the multilayer slab from those of a single layer. As a demonstration of applications of the formalism, we calculate the band structures of elastic waves propagating in a three-dimensional periodic arrangement of spherical particles and voids, as well as the transmission coefficients through finite slabs. In contrast with the plane-wave method, the multiple-scattering approach exhibits advantages in handling specialized geometries (spherical geometry in the present case). We also present a comparison between theory and ultrasound experiment for a hexagonal-close-packed array of steel balls immersed in water. Excellent agreement is obtained.