RESPONSE OF A PERIODICALLY DRIVEN IMPACT OSCILLATOR

The response of a single-degree-of-freedom oscillator that can impact a surface with prescribed harmonic motion is investigated through experimental and numerical means. The test apparatus consisted of a stainless steel cantilever beam that could collide with a voice coil shaker which was driven at a specified frequency and amplitude. By collocating the contact and measurement points at a particular location near the free end of the beam, the response was dominated by the beam’s fundamental mode. Response time records, frequency spectra and state space trajectories that were measured are compared to those predicted by a non-linear recurrence relation for the oscillator’s state from one impact to the next. As borne out by non-dimensionalization of the model, the amplitude of response at a given frequency of excitation is proportional to the amplitude of the surface’s motion, notwithstanding the non-linearity of the impact process. On the other hand, the qualitative character of the oscillator’s response depends strongly on the frequency of the surface’s motion. As the excitation frequency is increased gradually over a range equalling several times the oscillator’s natural frequency, the response exhibits a recurring pattern of resonance, period-doubling bifurcation, and irregular non-periodic motion. © 1994 Academic Press Limited.