About a stability conjecture concerning unilateral contact with friction

Elaine Pratt (1) , Alain Léger (2) , Michel Jean (2)

1 I2M - Institut de Mathématiques de Marseille
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

We study the qualitative dynamics of a simple mass-spring system involving non regularized unilateral contact and Coulomb friction and submitted to an oscillating external force. The period-amplitude plane of the excitation appears to be essentially divided into two ranges of sliding solutions. At each point of the lower range there exist infinitely many equilibrium points and all the trajec-tories go to equilibrium in finite time. In the upper range, there no longer exist equilibria. Different kinds of periodic solutions are shown to exist in different zones and the transitions between these zones are explicitly computed. The upper boundary of this range, where the mass looses contact, is also computed and special attention is paid to the dependence of this upper boundary with respect to the period of the excitation.

Mots clés: Coulomb friction; Mass-spring systems; Nonsmooth dynamics; Stability; Unilateral contact

Domaines: Vibrations [physics.class-ph]

Elaine Pratt, Alain Léger, Michel Jean. About a stability conjecture concerning unilateral contact with friction. Nonlinear Dynamics, 2010, 59 (1-2), pp.73-94. ⟨10.1007/s11071-009-9522-z⟩. ⟨hal-01580814⟩