Polynomial Chaos for Modeling Multimodal Dynamical Systems Investigations on a Single Degree of Freedom System

Abstract

This study aims at pointing out the somehow complex behavior of the structural response of stochastic dynamical systems and consequently the difficulty to represent this behavior using spectral approaches. In the modeling of dynamical systems, uncertainties are present and they must be taken into account to improve the prediction of the models. It is very important to understand how they propagate and how random systems behave. The aim of this work is to find numerically the probability density function (PDF) of response amplitude of random linear mechanical systems when the stiffness is random.
Polynomial Chaos performance is first investigated for the propagation of uncertainties in several situations of stiffness variances for a damped single degree of freedom system. For some specific conditions of damping and stiffness variances, it is found that numerical difficulties occur for the Hermite polynomial basis near the resonant frequency. Reasons come from the particular shape of the PDF of the response of the system that can present multimodality. Other bases are then investigated with no better results. Finally a multi-element approach is applied in order to gain robustness.