Exact Transient Solution of Some Problems of Elastic Wave Propagation

Citation

Flinn, Edward Ambrose (1960) Exact Transient Solution of Some Problems of Elastic Wave Propagation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QRYY-CD29. https://resolver.caltech.edu/CaltechETD:etd-02212006-132324

Abstract

Exact solutions are obtained for three problems of progressive elastic wave propagation in bounded media: (1) SH wave propagation from an impulsive point source in an infinite plate; (2) torsional waves in a solid cylinder; (3) radiation from an impulsive source of compressional and of shear waves in an infinite solid plate held between smooth rigid surfaces. The Laplace transform method is used. Problems (1) and (3) are shown to be closely related. For these problems the solution is expressed both as an infinite series of normal modes and an infinite series of multiple reflections, and it is shown that the two representations of the solution are related by Poisson's summation formula. Solutions are obtained for both a delta-function and a unit function input. Problem (2) is solved as an infinite series of normal modes for an impulsive shear stress source distributed over a normal section of the cylinder. The case of a point source on the axis of the cylinder is examined in detail. Problem (3) involves mixed boundary conditions. A relation between the solution of this problem and wave propagation in a free plate is discussed.

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