Stochastic models for uncertain flexible systems

Abstract

If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexible systems. Three typical examples of flexible beams with bilinear white noise perturbations are analysed in detail and conditions are given for the existence of a steady state covariance operator.