Acoustic response of a periodic layer of nearly rigid spherical inclusions in an elastic solid

Abstract

Reflection and transmission spectra of a plane longitudinal wave normally incident on a periodic (square) array of identical spherical particles in a polyester matrix are measured at wavelengths which are comparable to the particle radius and the interparticle distance. The spectra are characterized by several resonances whose frequencies are close to the cutoff frequencies for the shear wave diffraction orders. Arrays of heavy particles (lead and steel) exhibit a pronounced resonance which occurs when the lattice resonant frequency is close to the frequency of the rigid-body translation (dipole) resonance of an isolated sphere in an unbounded matrix. An approximate low-frequency theory is developed which assumes that the inclusions are rigid, but which takes into account the multiple-scattering effect. The comparison between theory and the experiment is found to be good for arrays with particle area fraction as high as 32%.