Flow switching bifurcations on the separation boundary in discontinuous dynamical systems with flow barriers

Abstract

In this paper, the flow passability on the separation boundary is investigated in discontinuous dynamic systems with flow barriers. The concepts of the flow barriers in discontinuous dynamical systems are introduced first. Because of the flow barriers existing on the separation boundary, the singularities of the flow on such a separation boundary will be changed accordingly. Therefore, the switching bifurcations from passable to non-passable flow or from non-passable to passable flow on the discontinuous boundary are discussed in this paper. Further, the necessary and sufficient conditions for the switching bifurcation and sliding fragmentation in discontinuous dynamical systems with flow barriers are developed. A periodically forced friction oscillator with static dry-friction is investigated as a sample problem for illustration of a flow into the flow barrier. This sample problem can be used to the cutting dynamics in manufacturing and brake system in automobile industry. This paper presents an efficient method to determine the flow passability on the boundary in discontinuous dynamical systems. The sliding mode control can be easily realized through the appropriate conditions as in this paper.