Elastic Waves Produced by Surface Displacements

Abstract

Waves produced in a homogeneous elastic body by time-dependent displacements of all or part of the body surface are determined by the geometrical theory of diffraction. Waves associated with the rays of geometrical acoustics, and with certain diffracted rays, are treated. The latter arise from curves of discontinuity of the applied displacement and from curves separating the displaced part of the surface from the free part. The expression for each type of diffracted wave contains a diffraction coefficient. Certain diffraction coefficients are determined from appropriate canonical problems which are solved exactly by the conical field method. The theory is applied to the impulsive and time-harmonic angular displacements of a circular region on the otherwise stress free surface of a half-space. The results are shown to agree with and extend those found previously in these cases by other methods.