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The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

Analytical solutions of three problems in coupled thermoelasticity are presented for the case when the material coupling parameter equals unity. The problems considered are: (a) Danilovskaya’s problem of a step function in temperature at the surface; (b) a step function in surface strain; and (c) constant velocity impact. Solutions are presented for the case of thin bars (one-dimensional stress) and are obtained by the Laplace-transform technique. There is great simplification in the equations when the material coupling parameter equals unity which permits the straightforward inversion of the transformed solutions. The results demonstrate significant deviations from the corresponding uncoupled solutions.

In this paper the stability theory of impulsive parametric excitation developed in [1] is first applied to three mechanical systems. Explicit and exact stability conditions are easily found and some typical stability charts are presented. Also presented in the paper is the use of this theory and a parallel theory involving step functions as approximate methods for treating periodic parametric excitations of more general nature. Exploratory studies along this line have led us to believe that these approximate methods have promise to be very powerful and practical tools for dealing with the stability of general high-order periodic systems.