On the periodic solutions of a non smooth dynamical system

Alain Leger (1) , Elaine Pratt (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

A simple mass spring system with non regularized unilateral contact and friction conditions is submitted to an oscillating loading. The behaviour of this system is represented in the period-amplitude plane. We first observe the existence of stationary solutions despite the oscillating loading in a whole strip of this plane. For larger amplitudes of the loading, stationary solutions no longer exist and we prove the existence of sliding periodic solutions of which the multiplicity, the period and the smoothness depend on the period of the loading. We then compute the boundary of the range where these sliding periodic solutions exist, and we show that beyond this boundary, periodic solutions still exist but loose contact during a part of the period, so that impacts must be correctly taken into account.

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

Alain Leger, Elaine Pratt. On the periodic solutions of a non smooth dynamical system. Revue de Mécanique Appliquée et Théorique, 2011, 2 (5), pp.511-522. ⟨hal-00835498⟩