Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach

In this paper, a friction system with uncertain parameters and coupled to two Nonlinear Energy Sinks (NESs) is studied. The dispersion of some physical parameters due to their uncertain nature may generate a dynamic instability which leads to a Limit Cycle Oscillations (LCO) causing a propensity of squeal. The concept of Targeted Energy Transfer (TET) by means of NESs to mitigate this squealing noise is proposed. In this kind of unstable dynamical system coupled to NES, the transition from harmless regimes (i.e. the LCO is mitigated) to harmful regimes (i.e. the LCO is not mitigated) as a function of the uncertain parameters implies a discontinuity in the steady-state amplitude profiles. In this context, a Multi-Element generalized Polynomial Chaos (ME-gPC) based method is proposed to locate this discontinuity (called mitigation limit) and therefore to predict the Propensity of the system to undergo an Harmless Steady-State Regime (PHSSR). The results obtained with this original method lead to a good compromise between computational cost and accuracy in comparison with a reference method.