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In this paper the problem of the interaction of an underwater explosion wave with a steel plate is discussed. Particular attention is given to those aspects of the problem in which the plate can be considered as an elastic, two-dimensional wave guide. The phase velocities of the more important modes of the plate are evaluated as functions of frequency. They are used to derive the properties of the precursor, an oscillation which precedes the explosion wave as it travels along the plate. The results of the theory are compared briefly with experiment. A more detailed discussion of the experiments will be given in a second report. The methods used in this report are also applicable to the evaluation of the phase velocities of the modes of an electromagnetic-wave guide. The propagation of a transient, such as an explosion wave, down a wave guide, presents the interesting mathematical problem of the evaluation of a contour integral of a function of a complex variable defined implicitly. No rigorous solution for this problem as yet exists.
Osborne et al. (Sun,) studied this question.