On discontinuous dynamics of a periodically forced double-belt friction oscillator

In this paper, complex discontinuous dynamics of a periodically forced double-belt friction oscillator are investigated using the theory of flow switchability for discontinuous dynamical systems. Phase plane of such a system is divided into different domains and boundaries due to the discontinuity caused by the friction and the positions of belts. The analytical conditions of the passable, stick and grazing motions on the corresponding discontinuous boundaries are derived for motion switching complexity in detail. Based on the discontinuous boundaries, switching sets and basic mappings are introduced to describe different periodic motions in such a discontinuous dynamical system. The analytical predictions and corresponding local stability analyses for the periodic motions are developed through mapping structures. Stick and non-stick periodic motions with different mapping structures, stick motions and grazing motions on different discontinuous boundaries are presented numerically for a better understanding of physics of the double-belt friction oscillator.