Exact transient solutions of buried dynamic point forces and displacement jumps for an elastic half space

Abstract

The exact transient closed form solutions for applying time-dependent point forces and displacement jumps at a depth below the surface of an elastic half plane are obtained in this study. A new methodology for constructing the reflected field is proposed and is shown to be both powerful and efficient. The solution of an exponentially distributed loading in the Laplace transform domain at the surface of a half plane is considered as the fundamental solution. The waves reflected from the free surface caused by the incident waves can be constructed by superimposing the fundamental solution. The numerical results of stress and displacement fields during the transient process are obtained and compared with the corresponding static value. It is shown in this study that the dynamic transient solution will approach the static value after the last reflected wave has passed.