Estimation of the Non-linear Limit Cycles of Autonomous Mechanical Systems Based on a Constrained Non-linear Approach

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

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

In this paper, a non-linear method for determining limit cycles of non-linear models of autonomous mechanical structures is proposed. Using approximations in the form of truncated Fourier series, the resolution of differential equations is changed into the minimization of specific functions. Not only the Fourier coefficients are obtained but also the fundamental frequency of the non-linear system is estimated. Moreover, this non-linear method allows the determination of the stable and unstable limit cycles of non-linear systems subject to flutter instability. In order to show the efficiency of this non-linear approach, the method is firstly applied on one- and two-degrees-of-freedom example models subject to flutter instability. Then, the non-linear dynamic of the Lorentz' chaotic system is investigated. The obtained limit cycles are compared to time integration in terms of accuracy and computing time.

Mots clés: Vibration; Limit Cycles; Non-linear Method

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Benjamin Hervé, Jean-Jacques Sinou, Hervé Mahé, Louis Jézéquel. Estimation of the Non-linear Limit Cycles of Autonomous Mechanical Systems Based on a Constrained Non-linear Approach. International Review of Mechanical Engineering, 2007, 1 (4), pp.356-362. ⟨hal-00323883⟩