Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass M through the analysis of the corresponding vector fields and G-functions. The periodic motions of such a discontinuous systemare predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.