Transient Analysis of Stress-Wave Penetration in Plates

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Abstract
This paper carries out an analysis of the propagation of a transient stress pulse concentrated at a point on the boundary of a plate whose thickness is of the order of a wave length. It is based on an expansion method used by Caignard in geophysical-layer problems which obviates the contour-integration difficulties and whose terms represent successively reflected waves of increasing time delay. From the general formulas obtained in this paper for an arbitrary forcing function, the stress versus time distribution along the axis of a 1-in-thick aluminum plate is obtained for a 5-microsec exponentially decaying pressure pulse. Inside the plate it is found there is a compressed zone which is relieved by a negative front traveling with the distortional wave velocity. When this interferes with a certain reflected negative front, the stress reverses in sign. A comparison of the location of this reversal is made with those based on plane-wave assumptions. Limiting cases are discussed.

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