Response of prestressed simply supported rectangular plates to random transverse uniform pressure

Abstract

The method of equivalent linearization and the Markov-vector approach are applied to the problem of the single mode nonlinear response of a stretched or compressed simply supported plate subjected to random uniform pressure. Closed form results are obtained for the latter solution in terms of parabolic cylinder functions which are tabulated and whose asymptotic forms are known. RMS values of maximum deflection and stress calculated by the two methods are compared and are found to be in excellent agreement provided the plate has not buckled. For buckled plates the two methods yield values which differ significantly for low values of loading spectral density.