Bifurcation Phenomena in a Mechanical Impact Vibration System with Periodic Boundary Conditions

Abstract

In this paper, an experimental apparatus was constructed to experimentally investigate whether the phenomenon of stepwise bifurcation occurs in mechanical vibration systems by applying periodic impact vibrations to a mass with a spring. In the experiment, the amplitude of the shaker was kept nearly constant, the frequency is varied, and the displacements of the shaker and the vibrating mass pushed by the shaker are measured. The results shows a trend similar to the stepwise bifurcation that occurred in the bouncing ball system. Before the stepwise bifurcation occurs, the vibrating body behaves similarly to a periodic vibration, but just before the stepwise bifurcation occurs, the amplitude of the vibration becomes smaller and non-periodic. After the stepwise bifurcation, the vibrating body vibrates non-periodically.