PERIODIC AND STOCHASTIC SELF-EXCITED OSCILLATIONS IN A SYSTEM WITH HEREDITARY-TYPE DRY FRICTION

The self-excited oscillations of an oscillator which is coupled by dry friction to a base moving at a constant velocity (Fig. 1) is consider ed. It is assumed that the coefficient of sliding friction f is const ant and that the coefficient of static friction is a piecewise-linear function of the duration t(k) of the preceding interval of prolonged c ontact between the body and the base (Fig. 2) [1]. A classification of the simplest periodic and steady-state stochastic self-excited oscill ations of the oscillator is given and the domains of their existence i n the parameter space of the system are constructed. The domains of tr ansient-type motion, within which periodic modes of arbitrary complexi ty exist, are analysed in detail. In particular, the equations of the so-called inaccessible boundaries [2] are constructed in explicit form . A denumerable set of different periodic trajectories of the dynamica l system under consideration exists in a small neighbourhood of these boundaries. (C) 1997 Elsevier Science Ltd.