Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings

Abstract

Exact and closed-form solutions are obtained for both tangential and vertical surface displacements of a homogeneous isotropic elastic half-space due to the application, at a point on the surface, of a concentrated force tangential to the plane boundary and varying with time as the Heaviside unit function. Similar expressions for the displacements in the interior of the body along a line directly below the applied force are derived. Solutions are obtained by a semi-inverse method with the aid of Laplace and Hankel transforms. The reciprocal relation in the static case, between tangential displacement due to a vertical force and vertical displacement due to a tangential force, is preserved in the dynamic case.