Response of an Elastic Half Space to a Decelerating Surface Point Load

Abstract

The displacement field on the surface of an elastic half space (Poisson ratio = 1/4), caused by the motion of a decelerating point surface load, is investigated by means of the dynamic Betti-Rayleigh reciprocal theorem. The load is applied impulsively and made to move rectilinearly at constant deceleration along the surface. The load speed varies from superseismic to a value less than the Rayleigh wave speed. The results show that significant differences exist between displacements obtained in this problem and those resulting from the usual assumption of constant load speed. The differences are primarily due to the presence of Mach cones which appear at superseismic load speeds and remain ahead of the initial wave fronts even after the speed becomes subseismic.