Analysis and Application of Bifurcations in Systems with Impacts and Chattering.

Abstract

In this Thesis we present the implementation and characterization of a practical impact oscillator: the cam-follower system. Complex dynamics experienced by the system after variation of the rotational speed of the cam taken as parameter, are analyzed through experimental, numerical and analytical tools. The most representative feature captured experimentally and reproduced after accurate simulation of the model, is the coexistence between a single-impacting periodic orbit and a multi-impacting trajectory with chattering, all of this occurring over a representative range of parameter values. Exhaustive numerical and analytical investigation including: Monte Carlo simulations, numerical continuation, calculation of basins of attraction and local analysis of perturbations, allowed to demonstrate that the interruption of complete chattering motion creates a sudden transition to chaos in the multi-impacting orbit characterized by a scaled and translated sequence of grazing bifurcations. An expression for the map local to the interruption of complete chattering is derived after performing expansion in series of the solutions; i.e. by analysis of variational equations, with further numerical validation. Additional work includes the extension of the local results for an accurate derivation of the equivalent Poincare map describing the periodic chattering orbit.