INTERMITTENCY IN IMPACT OSCILLATORS CLOSE TO RESONANCE

We examine the change in behaviour of the solutions of a simple one de gree of freedom, periodically forced, impact oscillator following a gr azing bifurcation in which an impact of zero velocity occurs following a change in one of the parameters of the system. It is shown that suc h a bifurcation leads to intermittent chaotic behaviour with low veloc ity impacts followed by an irregular sequence of high velocity impacts . We also show that there is a natural, discontinuous one-dimensional map associated with this relating one low velocity impact to the next and the properties of this map are analysed. We also construct the bif urcation diagram of the change in behaviour and show that this contain s a series of periodic windows, with the period of the solutions incre asing monotonically by one in each successive window as the bifurcatio n point is approached. By restricting our attention to the resonant ca se where the forcing frequency is twice the natural frequency of the o scillator it is possible to make asymptotic estimates of the form of t he intermittent chaotic behaviour and these estimates are compared wit h some numerical calculations.