Homogenization in three-dimensional phononic crystals

Abstract

We use a simple model to determine the frequency-dependent effective elastic coefficients of a three-dimensional phononic crystal, consisting of periodically arranged solid spheres embedded in fluid host, through theoretical calculations of the transmission coefficient and frequency band structure diagrams, using multiple-scattering techniques. Our results are successfully compared to those obtained from effective medium theories at the long wavelength limit. © 2007 IOP Publishing Ltd.