THE EFFECT OF FREQUENCY AND CLEARANCE VARIATIONS ON SINGLE-DEGREE-OF-FREEDOM IMPACT OSCILLATORS

A simple piecewise linear forced oscillator with impacts is taken as a model for more complicated vibro-impacting systems. The presence of i mpacts makes the system discontinuous and non-linear and to study it e ffectively the theory of dynamical systems is used. By a combination o f analytical and numerical techniques, many phenomena are identified w hich are characteristic of non-linear dynamical systems as the system parameters are varied. In particular, these include chaotic regimes an d multiply coexisting stable states. The domains of attraction of the periodic states are plotted and compared with the strange attractors o f the chaotic states. In addition, phenomena are observed related to t he discontinuity which have no counterpart in smooth dynamical systems ; chatter, when infinitely many impacts occur in a finite time, and gr azing, when a stable periodic orbit encounters a discontinuity and dis appears catastrophically under a smooth change in the parameters.