A fully nonlinear oscillator with contact and friction

Alain Léger (1) , Elaine Pratt (1) , Qingjie Cao (2)

1 M&S - Matériaux et Structures
2 HIT - School of Civil Engineering [Harbin]

In order to understand the effects of the coupling between smooth and nonsmooth nonlinearities in dynamical systems, we introduce a simple mechanical model containing the exact expression of nonlinear strains together with non-regularized unilateral contact and Coulomb friction conditions. This model is suggested both by previous work dealing with unilateral contact conditions and by work closer to classical dynamical systems which has recently led to the introduction of a new attractor. The main part of the paper concerns the investigation of the set of equilibrium states which turns out to be much more intricate than when the strains were linearized. Then the paper ends by suggesting some possible paths towards the study of the stability of these equilibria and of the qualitative dynamics.

Mots clés: Coulomb friction; Equilibrium states; Mass-spring system; Nonsmooth dynamics; SD-oscillator; Unilateral contact

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

Alain Léger, Elaine Pratt, Qingjie Cao. A fully nonlinear oscillator with contact and friction. Nonlinear Dynamics, 2012, 70 (1), pp.511-522. ⟨10.1007/s11071-012-0471-6⟩. ⟨hal-00835333⟩