On the Complex Dynamics of Nonlinear Systems with Viscous and Dry Friction with Memory

Abstract

A dynamical system consisting of a pair of bodies in frictional contact is considered. One of the bodies moves with a constant velocity, whereas the other is attached to a fixed support. The friction force is assumed as a sum of two friction forces: dry friction and viscous friction. The coefficient of the static friction is represented in the form of a piecewise linear function of the duration of the stick phase, whereas the coefficient of the kinetic friction is assumed to be constant. The qualitative structure of the phase space is studied in detail with qualitative methods, depending on the values of the coefficients of viscous friction and relative rest friction. The study is focused on the effect of the coefficients of viscous and dry friction. It is proven that the dynamical regime that include the stick phase occur only in certain parameter ranges. The mapping function is derived analytically and is shown to be a piecewise continuous function of the stick phase. The main regimes of periodic and stochastic motions are obtained by a semi-analytical method. The bifurcation diagrams are employed in order to study these regimes under various system parameters.