Diffraction of a plane harmonic Rayleigh wave on a circular elastic inclusion in elastic half-space (Q2753463)

The problem of diffraction of the plane harmonic Rayleigh wave on a circular elastic inclusion in elastic half-plane is considered. The method of solution is based on application of discontinuous solutions of Lamé equations for plane strain obtained using the Fourier transform. The total displacement field is represented as a superposition of two such solutions. The first solution is discontinuous at the half-plane boundary, and the second one is discontinuous at the inclusion boundary. In the result, the problem is reduced to an infinite system of algebraic equations. After its solution one can determine the unknown jumps that enter discontinuous solutions. Numerical investigation of stresses in the domain of interaction of solution with surrounding medium is carried out.