Energy Transfer in Vibratory Systems with Friction Exhibiting Low-velocity Collisions

Abstract

This paper investigates the dynamic response of an initially stationary part of a mechanism in the presence of a restoring force and dry friction to low-velocity collisions with a relatively more massive oscillating element. Of particular interest is the persistence of a local attractor in the motion of the less massive part as the path of the oscillating element grows to encompass the entire set of possible equilibrium positions in the absence of contact. It is argued that loss of a local attractor and the associated large-amplitude oscillations of the less massive part affords a means for energy transfer through the mechanism and a means for energy damping. The paper contains a rigorous derivation of conditions that appear sufficient for the persistence of a local attractor in the case where the massive oscillating element is replaced by an oscillating rigid unilateral constraint corresponding to an infinite mass ratio. Numerical simulations are subsequently used to investigate the response in the case where the mass ratio is assumed finite.