Elastodynamic response of a coplanar periodic layer of elastic spherical inclusions

Abstract

Reflection and transmission spectra of a plane longitudinal wave normally incident on a coplanar periodic array of identical spherical elastic inclusions in a solid (polyester) matrix are measured at wavelengths that are comparable to the inter-particle distance. These spectra exhibit pronounced Wood's anomalies i.e., a sharp variations in amplitude at the onset of a shear wave diffraction order as well as a drop in the transmission and a corresponding maximum in the reflection coefficients due to an enhancement of the resonance of the particles (for the case reported herein, this is the rigid body translational “dipole” resonance). An approximate low frequency ( ka<1) self-consistent model is developed in which multiple scattering is explicitly taken into account by adding appropriate terms to the well-known solution for the scattering of a plane longitudinal wave by a single spherical particle in an unbounded matrix. The results of the numerical calculations show excellent agreement with the experimental data.