Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal

This paper is devoted to the computation of nonlinear dynamic steady-state solutions of autonomous systems subjected to multi-instabilities and proposes a new nonlinear method for predicting periodic and quasi-periodic solutions intended for application to the disc brake squeal phenomenon. Firstly, finite element models of a pad and a disc are reduced to include only their contact nodes by using a Craig and Bampton strategy. Secondly, a complex eigenvalue analysis is performed showing two unstable modes for a wide range of friction coefficients, after which a Generalized Constrained Harmonic Balance Method (GCHBM) is presented. This method can compute nonlinear periodic or pseudo-periodic responses depending on the number of unstable frequencies. The numerical results are in good agreement with those of time marching methods.