Robustness of stochastic expansions for the stability of uncertain nonlinear dynamical systems - Application to brake squeal

This paper is devoted to the prediction and analysis of brake squeal under random uncertainty. This problem, which is a particular application of a wider issue, namely the stability of random parameter-dependent (RPD) nonlinear dynamical systems, is undertaken by using the non-intrusive generalized polynomial chaos (GPC) and Wiener-Haar expansions. The main objective is to assess the capacities of these meta-models within this framework. A reduced nonlinear non-equally damped, iso-damped and non-damped, disc/pad models are considered in this perspective in order to analyze the robustness of the proposed meta-models with respect to perfect and non-perfect mode coalescence. It turns out that the Wiener-Haar meta-model shows a more robust performance than GPC expansion and consequently offers a more reliable tool for the nonlinear stability analysis and thus for the prediction of brake squeal under parameter uncertainty.