Robust optimization of nonlinear energy sinks used for mitigation of friction-induced limit cycle oscillations

This paper aims at proposing robust methods to optimize nonlinear energy sinks (NES) used for the mitigation of friction-induced vibrations due to mode coupling instabilities. The study is based on a mechanical system composed of two NES coupled to the well-known two-degrees-of-freedom Hulten's model. In such an unstable system coupled with NES, it is usual to observe a discontinuity in the steady-state amplitude profile which separates the parameter space into two parts corresponding respectively to the mitigated and unmitigated regimes. The discontinuity is predicted by a methodology previously developed by the authors and based on Multi-Element generalized Polynomial Chaos. The method allows to determine the Propensity of the system to undergo a Harmless Steady-State Regime (PHSSR). The objective of the present work is therefore to maximize the value of the PHSSR to obtain a robust optimal design of the NES. To this end, several stochastic optimization problems are presented that take into account the dispersion of the uncertain parameters using two approaches; in the first one, the parameters of the NES are considered as deterministic, and in the second one they are also supposed uncertain but with a known probability law.