Investigation of Rayleigh wave interaction with surface defects

Abstract

The current article is concerned with the interaction of Rayleigh waves with surface defects of arbitrary shape in a homogeneous, isotropic, linearly elastic half-space. Using a linear superposition principle, the interaction generates a scattered field which is equivalent to the field radiated from a distribution of horizontal and vertical tractions on the surface of the defect. These tractions are equal in magnitude but opposite in sign to the corresponding tractions obtained from the incident wave. The scattered field is then computed as the superposition of the displacements radiated from the tractions at every point of the defect surface using the reciprocity theorem approach. The far-field vertical displacements are compared with calculations obtained by the boundary element method (BEM) for circular, rectangular, triangular and arbitrary-shaped defects. Comparisons between the theoretical and BEM results, which are graphically displayed, are in excellent agreement. It is also discussed the limitations of the proposed approximate theory. Keywords: half-space; Rayleigh wave; surface defect; reciprocity theorem; boundary element method (BEM).