Analysis of stochastic structures : Perturbation method and projection on homogeneous chaos

Abstract

The goal of this paper is to analyze the modal characteristics of structures including random parameters. We compute the mean value and the standard deviation of the eigenvalues and also of the transfer functions. Two main techniques are used o do so. The first one is based on the Taylor Series procedure and the second one on the Polynomial Chaos. Limits of both approaches are studied in terms of sensitivity of the solution (modal parameters and transfer functions) versus the random parameters values. A Monte Carlo Simulation is used to validate out results obtained by the two methods . If we are interested in solving industrial problems then these techniques are too much time consuming. In order to avoid this drawback, it becomes necessary to reduce the number of degrees of free-dom of the model. A way to reduce the size of the problem is to use a modal synthesis approach extended to the case of structures defined by stochastic parameters. We emphasize the efficiency of this procedure in the estimation of the mean value and the standard deviation of the modal parameters and lie transfer function.