Analysis of discontinuous dynamical behavior of a class of friction oscillators with impact

In this paper, the discontinuous dynamical behaviors in the friction oscillator with impact are investigated by using the theory of flow switchability in discontinuous dynamical systems. On the basis of discontinuity of friction and impact, different domains and boundaries are defined for such system. Based on above domains and boundaries, the analytical conditions of passable motion, stick motion, sliding motion and grazing motion are obtained mathematically. The analytical predictions of the corresponding periodic motion are given by the adequate mapping structures. The passable, stick, sliding, grazing and periodic motions are illustrated through trajectories in phase planes and time histories of displacement, velocity and G-function for a better understanding of motion mechanism of the friction oscillator with impact. In the end, the grazing and sliding bifurcations are determined by the local singularity theory of discontinuous dynamical systems. This model is suitable for nonlinear dynamical description of the vibration in rotor bearing or gear transmission systems with impact and friction.