Extension of the destabilization paradox to limit cycle amplitudes for a nonlinear self-excited system subject to gyroscopic and circulatory actions

Benjamin Hervé (1, 2) , Jean-Jacques Sinou (1) , Hervé Mahé (2) , Louis Jezequel (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 Valéo Transmission

This study aims at clarifying the phenomenological roots of an acoustical disturbance known as "clutch squeal noise". A nonlinear two-degrees-of-freedom model is introduced in order to illustrate some basic phenomena leading to self-generated vibrations. The damping of the system as well as both circulatory and gyroscopic actions are included in order to highlight their respective influence and the destabilization paradox. Results are obtained on the stability range of the equilibrium, the nature of the Hopf bifurcation, the limit cycle branches and their stability. A dynamic extension of the destabilization paradox is proposed and some non-periodic behaviours are identified too.

Mots clés: non-linear vibration; stability; friction

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

Benjamin Hervé, Jean-Jacques Sinou, Hervé Mahé, Louis Jezequel. Extension of the destabilization paradox to limit cycle amplitudes for a nonlinear self-excited system subject to gyroscopic and circulatory actions. Journal of Sound and Vibration, 2009, 323 (3-5,), pp.944-973. ⟨10.1016/j.jsv.2009.01.023⟩. ⟨hal-00411721⟩