A formalism is presented for the solution of supported plates of bounded extent, subjected to time-dependent transverse forces and boundary conditions. Initially, and during the course of the motion, the plate is assumed to be in an arbitrary (stable) state of membrane stress. An example of a suddenly loaded, simply supported rectangular plate is presented. The membrane prestress, in the example problem, is assumed to be constant and parallel to two opposite edges of the plate.
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Reismann et al. (1976) studied this question.