Scattering of elastic waves by a periodic monolayer of spheres

Abstract

Using the multiple-scattering formalism we developed in a previous work, and extended here, we analyze available experimental data on the transmission of longitudinal waves in the system: water-slab of polyester-water, the slab of polyester having a plane of glass or lead or steel spheres in the middle. The theoretical results reproduce accurately the measured spectra and provide a transparent physical picture of the underlying processes. In particular, the dips in the observed spectra are attributed to multiple wave scattering between the spheres, and are related to hybridization-induced gaps in the frequency band structure of the longitudinal elastic modes of a corresponding infinite crystal.