A half-space response to a finite surface source of an impulsive disturbance

Abstract

The response of an ideal elastic half-space to an impulsive load is obtained by a computational method based on the theory of characteristics. The impulsive load is distributede unevenly but radially over the entire boundary of a semicircular infinite canyon embedded in the surface of the half-space. For this configuration, a wave characteristics formulation is presented where its differential equations are extended to accommodate strong discontinuities which occur in the material motion of the half-space. A step-by-step numerical integration of these extended differential equations is then carried out in a two-dimensional curvilinear wavegrid, formed by the bicharacteristic curves of the wave characteristics formulation. The resultant transient deformation of the half-space is shown by plots which give the time history behavior of the dependent variables at a specific spatial location. In these plots, the various wave fronts traversing the half-space explicitly reveal themselves.