Controlled onset of low-velocity collisions in a vibro-impacting system with friction

Abstract

This paper investigates the onset of low-velocity, near-grazing collisions in an example vibro-impacting system with dry friction with particular emphasis on feedback control strategies that regulate the grazing-induced bifurcation behaviour. The example system is characterized by a twofold degeneracy of grazing contact along an extremal stick solution that is shown to result in a locally one-dimensional and piecewise-linear description of the near-grazing dynamics. Explicit control strategies are derived that ensure a persistent, low-impact-velocity, steady-state response across the critical parameter value corresponding to grazing contact even in instances where the dynamics in the absence of control exhibit a sudden transition to a high-impact-velocity response.