Transmission, Reflection, and Guiding of an Exponential Pulse by a Steel Plate in Water

The problem of the action of an underwater explosion—a pulse of the form pmaxe−t/τ—on an elastic plate in water can be divided into two parts. In the first, the plate is considered as an infinite slab with the explosion wave as an incident plane wave transient. In the second, the plate is considered as a wave guide, with the explosion wave setting the initial conditions at the edge of the plate. The first is an inhomogeneous boundary value problem, the second a homogeneous one. The inhomogeneous case has been solved in the literature, for continuous waves, and the results of the theory are in qualitative agreement with the experiments on transients. The homogeneous problem forms the principal part of this paper. The phase velocity curves, as functions of frequency, for the principal normal modes of a plate in water, are closely related to the corresponding curves for a plate in a vacuum. The effect of the water on the principal symmetric mode of the plate is not to change the real part of the phase veloci...