Transient response of an elastic plate to loads with finite characteristic dimensions

The present paper uses a recently developed technique to obtain solutions for an elastic plate acted upon by loads with finite characteristic dimensions. Exact two dimensional transform solutions are derived for a plate suddenly loaded on one of its bounding surfaces. The transform solutions for a general load are rearranged into infinite sums representing multiply-reflected shear and dilatational waves. The interpretation of the infinite sums is verified by ray tracing. The final expressions are used to deduce the Green's function for the velocity. Numerical results are presented for a step function input.