PULSE PROPAGATION IN AN ELASTIC PLATE WITH A BUILT-IN EDGE.
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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In a recent report the author presented a method for treating waveguide problems based on the equations of motion from linear elasticity theory, and involving non-mixed edge conditions the stresses or the displacements. In the method a Laplace transform, say parameter s, is used on the propagation coordinate, say x. To insure that a solution be bounded as x approaches infinity, residues at the poles of the transformed solution in the right half s-plane, and corresponding to complex wave number roots of the governing Rayleigh-Lamb frequency equation, are set equal to zero. This generates two coupled integral equations for the edge unknowns which depend, parametrically, on these complex wave number roots. Solution of these equations determines the transformed solution of the problem, which can be inverted through known techniques. In the present work this general method is used to solve the problem of a semi-infinite plate with a built-in edge, excited by suddenly applied symmetric normal line loads on its faces, and near the edge. The long time solution, for the near and far field is obtained, disclosing the nature of the reflection process at the edge. Interesting is the fact that the edge generates a pulse that in the far field is non-decaying in space and time, having the same form found in analogous dynamic edge or end load problems. Author
- Electrical and Electronic Equipment