Study of a transition in the qualitative behaviour of a simple oscillator with Coulomb friction

Elaine Pratt (1) , Alain Leger (1) , Xiang Zhang (2)

1 M&S - Matériaux et Structures
2 Department of mathematics and MOE-LSC

A simple mass-spring system is submitted to a constant force in addition to a periodic perturbation of rectangular wave shape. It has been obtained in a previous study that the range of the period-amplitude plane of this perturbation where the trajectories are sliding without jumps is divided into two parts, one in which there exist infinitely many equilibrium states and no periodic solutions, and another one where there exist periodic solutions and no equilibrium states. The present work focuses on the transition between these two parts. All along the transition line, there exists a single equilibrium state. Initial data out of equilibrium lead either to a periodic trajectory, or to a trajectory which tends to the equilibrium or to a periodic solution, either in finite time or at infinity.

Mots clés: Coulomb friction; Equilibrium states; Mass-spring systems; Nonsmooth dynamics

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

Elaine Pratt, Alain Leger, Xiang Zhang. Study of a transition in the qualitative behaviour of a simple oscillator with Coulomb friction. Nonlinear Dynamics, 2013, 74 (3), pp.517-531. ⟨10.1007/s11071-013-0985-6⟩. ⟨hal-00943154⟩