Pitfalls in the frequency response represented onto Polynomial Chaos for random SDOF mechanical systems

Abstract

• The frequency response function of a stochastic single-degree-offreedom oscillator is studied. • Conditions for which the probability density function is multimodal are established. • It is shown that Polynomial Chaos then fails to provide accurate results. • Outputbased approach and multi-element generalized Polynomial Chaos are shown to return satisfying results. Uncertainties are present in the modeling of dynamical systems 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. 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. The main objective is to find numerically the probability density function (PDF) of the response of a random linear mechanical systems. Since it is found that difficulties can occur even for a single-degree-of-freedom system when only the stiffness is random, this work focuses on this application to test several methods. 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 standard polynomial bases near the resonant frequency, where it is generally observed that the shape of the system response PDFs presents multimodality. Strategies to build enhanced bases are then proposed and investigated with varying degrees of success. Finally, a multi-element approach is used in order to gain robustness.