Stick and non-stick periodic motions in periodically forced oscillators with dry friction

In this paper, the force criteria for stick and non-stick motions in harmonically forced, friction-induced oscillators are developed from the local theory of non-smooth dynamical systems on connectable domains. The periodically driven, linear oscillator with a simple dry friction is considered as a sampled problem to demonstrate the methodology presented in this paper. With appropriate mapping structures, the force criteria give the analytical predictions of the stick and non-stick, periodic motions for such an oscillator. Furthermore, the effects of external excitations and friction forces on the stick and non-stick motions are discussed, and the corresponding regions of specified motions in parameter space are obtained. The sliding and grazing phenomena for this oscillator are also presented in this paper. However, an extensive investigation on sliding and grazing bifurcations should be carried out in sequel. The displacement, velocity and force responses for stick and non-stick, periodic motions are illustrated for a better understanding of the dynamics mechanism of stick and non-stick motions of the dry-friction oscillator. The force criteria and mapping techniques are also applicable to multi-body contact dynamics. The methodology presented in this paper can be applied for numerical predictions of motions in nonlinear, non-smooth dynamical systems.