FRICTIONAL SELF-OSCILLATIONS IN AN OSCILLATORY SYSTEM ACCOUNTING FOR HEREDITARY-TYPE FRICTION FORCES

Abstract

The dynamics of an oscillator consisting of a pair of friction surfaces, one of which is moving at a constant velocity and the other located on it is secured to a rigid support, is considered. The friction force is assumed as a sum of two friction forces: dry friction with the relative rest friction coefficient as a monotonously increasing function of the duration time of relative rest of the bodies of friction, and viscous friction with a constant friction coefficient (a hereditary-type friction force). The phase space structure as a function of the viscous friction coefficient value is studied; modes with relative rest of the friction surfaces are shown to be possible only for viscous friction coefficient values within a certain interval. An analytical form of Poincare function is given which makes it possible either to determine fixed points of the point map corresponding to periodic modes of body motion or to find bifurcation values of parameters of the onset of chaos.

Keywords: mathematical model, hereditary-type friction, Poincare function, relative rest, fixed point, chaos.