Diffraction of Transient Elastic Waves by a Spherical Cavity

Citation

Norwood, Frederick Reyes (1967) Diffraction of Transient Elastic Waves by a Spherical Cavity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ps9n-9z78. https://resolver.caltech.edu/CaltechETD:etd-10022002-110856

Abstract

The diffraction of transient elastic waves by a spherical cavity is treated. Two cases are considered: (a) a suddenly applied normal point load, and (b) the impingement of a plane transient pulse on the cavity. The method used determines the solution only in the shadow zones; that is, those points which cannot be connected to the source of disturbance by straight-line rays. Analytical results are obtained and evaluated for the displacements at the cavity wall.

The analysis is based on the Laplace transform (on time) and the Watson transformation. This well-known transformation makes it possible to convert an infinite series involving a discrete real wave number into one involving a generalized wave number. This leads to transient solutions the components of which have a one-to-one correspondence with the modes of the underlying frequency equation. These solutions have a form convenient for numerical analysis and for obtaining approximate solutions.

The results given here are for the displacements evaluated at the cavity wall. It is found that the behavior of the diffracted wave fronts is similar to that associated with the simpler equations governing scalar diffraction problems (see Friedlander, "Sound Pulses" , Cambridge, 1958). In both problems the Rayleigh disturbance predominates for long time, being singular at its arrival time in the point load case and non-singular in the plane wave case.

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