New limit cycles of dry friction oscillators under harmonic load

Abstract : We consider a system composed of two masses connected by linear springs. One of the masses is in contact with a driving belt moving at a constant velocity. Friction force, with Coulomb's characteristics, acts between the mass and the belt. Moreover, the mass is also subjected to a harmonic external force. Several periodic orbits including stick phases and slip phases are obtained. In particular, the existence of periodic orbits including a part where the mass in contact with the belt moves in the same direction at a higher speed than the belt itself is proved. Non-sticking orbits are also found for a non-moving belt. We prove that this kind of solution is symmetric in space and in time.