Scattering on a Small Inhomogeneity in an Elastic Medium

Abstract

Problems on the diffraction of elastic plane waves (transverse and longitudinal) scattered on a cylinder are investigated. The radius a of the cylinder is small enough (\(ka \ll 1\), where \(k\) is the wave number). The waves of horizontal polarization (SH waves) are scattered similarly to the electromagnetic wave of the respective polarization. It is proved that a small inhomogeneity radiates as a point source, with its amplitude proportional to the difference of the Lame parameters \(\mu _1\) and \(\mu _2\) and to the area of a cross section of the inhomogeneity. The scattering of a plane wave of vertical polarization is subject to a more complicated law of radiation, because of the vector nature of the problem, and the respective components of the displacement vector are represented in terms of the scalar and vector potentials. However, the scattering of the wave field on the small inhomogeneity has qualitatively the same asymptotic behavior as in the case of the SH wave. Bibliography: 4 titles.