Multiple Diffractions of Elastic Waves by a Rigid Rectangular Foundation: Plane-Strain Model

A rigid rectangular foundation embedded in an elastic half space moves in a direction perpendicular to the surface of the half space, Fig. 1. The model under consideration is of the plane-strain type. By application of the Laplace, Fourier, and Kontorovich-Lebedev (K-L) transforms, the equation of motion for the foundation is derived. The transient response of the foundation is exact during the period of time required for a longitudinal wave to traverse the base of the foundation twice. Thus the process of multiple diffractions at the corners of the foundation is taken into account.