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

Nicolas Coudeyras (1, 2) , Samuel Nacivet (2) , Jean-Jacques Sinou (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 PSA - PSA Peugeot - Citroën

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.

Mots clés: friction; non-linear dynamic; squeal

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Systèmes dynamiques [math.DS]

Nicolas Coudeyras, Samuel Nacivet, Jean-Jacques Sinou. Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal. Journal of Sound and Vibration, 2009, 328 (4-5), pp.520-540. ⟨10.1016/j.jsv.2009.08.017⟩. ⟨hal-00425156⟩