Stochastic study of a non-linear self-excited system with friction

This paper proposes two methods based on the Polynomial Chaos to carry out the stochastic study of a self-excited non-linear system with friction which is commonly used to represent brake-squeal phenomenon. These methods are illustrated using three uncertain configurations and validated using comparison with Monte Carlo simulation results. First, the stability of the static equilibrium point is examined by computing stochastic eigenvalues. Then, for unstable ranges of the equilibrium point, a constrained harmonic balance method is developed to determine subsequent limit cycles in the deterministic case; it is then adapted to the stochastic case. This demonstrates the effectiveness of the methods to fit complex eigenmodes as well as limit cycles dispersion with a good accuracy.

► A 2-dofs non-linear system with friction and 3 uncertain configurations are considered.
► 2 methods based on polynomial chaos and HBM are proposed.
► The stochastic eigenvalue problems are solved, investigating stability.
► Stochastic limit cycles on unstable ranges are evaluated.