Analysis of dynamical behaviors of a friction-induced oscillator with switching control law

In this paper, the dynamical behaviors of a friction-induced oscillator with switching control law are studied through the flow switching theory of discontinuous dynamical systems. The physical model consists of a mass on the conveyor belt and a spring-damping system with switching control law. Based on the switching control law and the friction between the oscillator and the conveyor belt, multiple domains and discontinuous boundaries are defined. The G-functions are introduced to illustrate the motion switching mechanism and the analytical conditions of the passable motion, stick motion, sliding motion and grazing motion are presented for motion switchability. The switching sets and mapping structures are adopted to describe the complex motions in this discontinuous system. The numerical simulations are also carried out from the analytical conditions and mapping structures in order to better understand the motion switching complexity of this oscillator.