Behavior of stochastic shear beams under random loading via stochastic variational principles

In this study we derive, apparently for the first time in the literature, s ome exact solutions for the shear beams with stochastic flexibility, when t hese beams are acted upon by the random loading. The importance of these so lutions lies in the fact that they can serve as benchmark solutions, to whi ch the approximate solutions of various nature can be compared. Then we for mulate stochastic variational principles, the first principle governs the b ehavior of the mean displacement, whereas the second principle is satisfied by the displacement's covariance function. These variational principles al low us to formulate approximate techniques for the cases in which the exact solution is presently unavailable. In particular, we develop a stochastic version of the Rayleigh-Ritz method. Several examples are evaluated to shed more light on the probabilistic behavior of randomly excited structures po ssessing random flexibility. (C) 1998 Elsevier Science Ltd. All rights rese rved.