Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties

Jérôme Didier (1) , Jean-Jacques Sinou (1) , Beatrice Faverjon (2)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

This paper presents the concept of the Stochastic Multi-dimensional Harmonic Balance Method (Stochastic-MHBM) in order to solve dynamical problems with non-regular nonlinearities in presence of uncertainties. To treat the nonlinearity in the stochastic and frequency domains, the Alternate Frequency-Time method with Probabilistic Collocation (AFTPC) is proposed. The approach is demonstrated using nonlinear two-degree-of-freedom model with different types of nonlinearities (cubic nonlinearity, contact/no contact, friction). The quasi-periodic stochastic dynamic response is evaluated considering uncertainties in linear and nonlinear parts of the mechanical system. The results are compared with those obtained from the classical Monte Carlo Simulation (MCS). For various numerical tests, it is found that the results agreed very well whilst requiring significantly less computation.

Mots clés: Stochastic Multi-dimensional Harmonic Balance Method; quasi-periodic; stochastic; dynamic response; uncertainties; nonlinear elements; nonlinearities; cubic stiffness; contact; friction

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

Jérôme Didier, Jean-Jacques Sinou, Beatrice Faverjon. Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties. Communications in Nonlinear Science and Numerical Simulation, 2013, 18 (11), pp.3250-3270. ⟨10.1016/j.cnsns.2013.03.005⟩. ⟨hal-00831862⟩