Scattering of a transverse elastic wave by an elastic sphere in a solid medium

Publisher Website
Google Scholar
Abstract
Cross sections are computed for the scattering of a plane transverse elastic wave by an elastic sphere in an infinite isotropic homogeneous elastic solid. Analytic expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K1a (K1 is the transverse propagation constant, a is the obstacle radius) over the range 0.01–10 is computed for various combinations of host and scatterer materials. The sensitivity of the cross section and its component terms to the elastic properties of the host and scatterer materials, and their behavior in the Rayleigh limit approximation are discussed. The calculations include the case of a constant host with a varying obstacle, and a constant scatterer in a varying host medium. It is found that most of the examples tested can be grouped conveniently into four classes, with a fifth category containing unstable results; this classification scheme is based on the general shape and specific peaking behavior of the cross‐section curves. The peaking behavior is related to the occurrence of zeros in the spherical Bessel and Neumann functions.