Normal Mode Variational Method for Two- And Three-Dimensional Acoustic Scattering in an Isotropic Plate

Abstract

A method is presented for solving two- and three-dimensional acoustic scattering problems in an infinite isotropic elastic plate. Two- and three-dimensional plate Green's functions have been developed in terms of plate elastic wave mode expansions, using the elastodynamic reciprocity relation to carry out the expansions. General properties of these Green's functions are discussed and they are applied to the formulation of thin crack scatterers. A variational principle is developed for the modal reflection coefficients and a numerical example is given. Problems of convergence and truncation of the mode expansion series are considered.