Effects of pre-stress on impact waves in an incompressible elastic plate

Abstract

We study the effects of pre-stress on the propagation of impact waves resulting from a sudden line load applied on the surface of an infinite isotropic incompressible elastic plate placed on a smooth rigid foundation. The pre-stress is assumed to be a uni-axial compression or an allround pressure (tension). Our interest is in the behaviour of the impact waves when the pre-stress approaches any of the critical values for buckling instability. The problem is solved using Laplace and Fourier transforms. The Laplace inversion is carried out analytically and the Fourier inversion is evaluated both numerically and with the aid of the method of stationary phase.