Random vibrations of orthotropic plates clamped or simply supported all round

Abstract

An approximate method is presented for determining the probabilistic response of rectangular orthotropic plates clamped all round. For solving the stochastic boundary value problem, the probabilistically given and sought functions are expressed in terms of series of approximate modes of vibration, which satisfy the boundary conditions but not the field equation. Galerkin's procedure then yields a set of linear equations for the cross-spectral densities of the displacements. The cross-spectral density of the external pressure is taken to be a product of longitudinal and transverse correlation coefficients which depend on frequency and separation distance. When the approximate method presented here is applied to cases capable of closed solutions (i.e. plates having a pair of opposite edges simply supported), the result coincides with that obtained by the classical normal-mode approach.