Transient analysis of a three-dimensional plate by the ray grouping technique☆

Abstract The propagation of transient waves in an elastic plate excited by an arbitrary loading is investigated. Exact three-dimensional transform solutions are derived for a plate suddenly loaded on one of its bounding surfaces, with the inversion effected by Cagniard's technique. The solution is based on three canonical problems for finding the n -th reflected waves from only the information on the ( n − 1)-th reflected waves. The technique automatically groups rays which arrive simultaneously at one point, thus simplifying the computations needed by the ray tracing technique. A nonaxially symmetric sample loading is selected for demonstrating the technique, and numerical results are presented. The Ray Grouping Technique can be extended to the layered medium case.