A Frictional Oscillator on Time-varying Belt

Abstract

In this chapter, an oscillator moving on a periodically traveling belt with dry friction is presented as a discontinuous dynamical system with a time-varying boundary. Such a time-varying boundary will cause the domain to change with time, on which the vector fields can be defined. From the theories in Chapter 2, analytical conditions for stick and non-stick motions on a periodically traveling belt in such an oscillator with dry friction will be developed, and the relative force product criteria will be obtained to predict such stick and non-stick motions. The grazing and stick (or sliding) bifurcations will be discussed for appearance and vanishing of regular motions in such an oscillator. Parameter maps for specific periodic motions will be obtained through mapping structures. The displacement, velocity and force responses of periodic motions will be presented to illustrate the analytical conditions of stick and non-stick motions.