On Solving Elastic Waveguide Problems Involving Non-Mixed Edge Conditions

摘要

Within the framework of the 'exact' linear theory an important class of wave propagation problems in elastic waveguides, involving non-mixed edge conditions (like stress or displacement), have remained unsolved. Basically, this is because known separation methods (classical or integral transforms) do not 'ask' in a natural way for the given edge information. A means for solving some problems in this class, focused on the semi-infinite plate, as an example, is presented here. In the method a Laplace transform is used on the propagation coordinate, say x. Exploitation of the boundedness condition on the solution, at x to infinity, generates two coupled integral equations for the edge unknowns (displacements and strains), which depend, parametrically, on those complex wave number roots of the governing Rayleigh-Lamb frequency equation representing unbounded waves. Solution of these equations determines the transformed solution of the problem, which can be inverted through known techniques. Excitation of a plate with a built-in edge is treated as an example. (Author)