ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS

Abstract

<abstract> In this paper, the analytical dynamics is investigated in a periodically forced friction oscillator under two-frequency excitations. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static friction force, $ G $-functions are defined through the dot product of the vector fields and the normal vector. By the sign of $ G $-functions, the necessary and sufficient conditions for the flow passibility and the grazing motions to the separation boundary are developed. For the examined system, the boundary possesses flow barriers caused by the static friction force. Because the flow barriers exist on the separation boundary, the singularities of the flow on such a separation boundary will be changed accordingly. Based on the critical values of flow barriers, the necessary and sufficient conditions for the onset and vanishing of the stick motions on the boundary with flow barriers are also developed. Furthermore, the periodic motions of such an oscillator are determined through the corresponding mapping structures. Illustrations of the periodic motions in such a piecewise friction model are given to verify the analytical conditions. </abstract>