Generalized Polynomial Chaos for robust modelling of Nonlinear Energy Sinks used to mitigate dynamic instabilities in braking systems

International audienceThis paper investigates the passive mitigation of a squeal noise problem in nonlinear dry friction systems with uncertain parameters by means of Nonlinear Energy Sinks (NESs). The study is based on a mechanical system which is composed of two ungrounded NESs attached to the well-known Hultèn's two degrees of freedom model. The random dispersions of the friction coefficient and the damping ratio make the system unstable. In fact, the sensitivity of these parameters is such that the steady state of the mechanical system is discontinuous and presents a jump. This jump induces areas in which the efficiency of the NESs is either high or low. Two approaches using generalized Polynomial Chaos (gPC) are developed to identify this jump and to predict the boundary values of the uncertain parameters for which the NESs can act or not. The gPC methods prove their capacities to predict the discontinuity. Thus, this analysis allows to estimate the Propensity to undergo an Harmless Steady-State Regime (PHSSR) of the oscillation by the NESs. Finally, the results are compared with the prohibitive Monte-Carlo (MC) method which is considered as the reference method. There is a good compromise between computational cost and accuracy using the gPC methods