Periodic motions of an impact oscillator

Non-linear equations governing N impact periodic motions of a single-degree-of-freedom oscillator under a sinusoidal and bias force contacting rigid amplitude constraints on one or both sides have been developed with constant and velocity dependent coefficients of restitution. They also govern period doubling motions. Additionally, exact closed form expressions have been developed for one and two equispaced and non-equispaced impacts per cycle motions. Theoretical predictions agreed with previous results and with results obtained using a numerical simulation approach. Effects of amplitude and frequency of sinusoidal force, bias force, damping, and variable and constant coefficients of restitution on periodic motions are investigated. (C) 1998 Academic Press Limited.