Analytical Dynamics of a Piecewise Linear Friction Oscillator Under a Periodic Excitation

Abstract

This paper presented a methodology to determine the analytical dynamics of the periodically forced friction oscillator. The friction force is modeled by a piecewise linear, kinetic friction model with the static force. The input and output force concepts in the vicinity of the discontinuous friction force boundary are introduced. The force criteria for the onset and vanishing of stick and non-stick motions are presented through the input and output forces. The periodic motion of such an oscillator is determined through the corresponding mapping structure. The local stability of the periodic motions is presented. Illustrations of the periodic motions in such a piecewise friction model are given for better understanding the stick motion with static friction. The force responses are presented, which agreed very well with the force criteria.