Reflection and Transmission by an Array of Spherical Voids in an Elastic Solid
Studies of scattering by porosity are often based on single scattering theory, in which the interaction between the voids is either neglected or taken into account in some approximate manner. In this paper we consider a case where the analysis can be carried out without approximations, and the effect of multiple scattering can be rigorously accounted for. The particular configuration concerns a doubly periodic array of spherical cavities in an elastic solid. The cavities are all of equal radius d, their centers are all located in a single plane (the x1-x2 -plane), and the centers are located at positions x1 = ma, x2 = nb, where −∞ < m,n < ∞, as shown in Fig. 1. The incident wave is a plane longitudinal wave which propagates in the x3 -direction.