Nonsmooth Bifurcations and Chaotic Transients in a Simple Frictional Oscillator

In this paper, we present a model of a single degree-of-freedom periodically forced oscillator that is damped by Coulomb-type friction. During the earlier examination of a similar model — with equal coefficients of sliding and sticking — only periodic steady-state solutions were found. In the present model, the two coefficients of friction are different. We show that this slight modification can lead to the occurrence of chaotic or transient chaotic behavior in certain parameter ranges, where the ratio of the sticking and sliding coefficients is quite large. Transient chaotic behavior is investigated in detail and finite time Lyapunov exponent is calculated. Moreover, a novel form of a sticking map is presented that enables the identification of nonsmooth bifurcations in the system.