ON SOLVING ELASTIC WAVEGUIDE PROBLEMS INVOLVING NON-MIXED EDGE CONDITIONS
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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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.
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