Diffraction of Plane Elastic Waves with Vertical Polarization on a Small Obstacle in a Layer

Abstract

The problem on the diffraction of elastic plane waves with vertical polarization on a small obstacle (elastic inhomogeneous inclusion) inside a layer is investigated. The layer is situated on an elastic half-space. A three-layer model of isotropic elastic media is considered. The obstacle is assumed to be a circular cylinder with radius that is small in comparison with the length of the incident wave. The polarization of the incident wave is assumed to be orthogonal to the axis of the cylinder. The diffractional addition on the small obstacle to the reflected wave in an elastic layer is proved to have a larger order than the order of the first term with respect to the parameter \({{\left( {ka} \right)^2 } \mathord{\left/ {\vphantom {{\left( {ka} \right)^2 } {\sqrt {kr} ,\;kr \gg 1,\;}}} \right. \kern-\nulldelimiterspace} {\sqrt {kr} ,\;kr \gg 1,\;}}kr \ll 1\), where \(k\) is the wave number, r is the distance between the obstacle and the observation point. The small obstacle generates a cylindrical wave the intensity of which is proportional to the area of the cross-section of the obstacle and to the jumps of the square velocities in the layer and in the obstacle. Bibliography: 6 titles.