Spiky structure in velocity distribution for a ball bouncing on a vertically vibrating plate

Abstract

We present the experimental and numerical results of velocity distribution for a ball bouncing on a vertically vibrating plate. The “spiky” structure is observed in the velocity distribution. According to the “energy” level obtained from the rescaled flight time of the ball, the formation of the “spiky” structure is analyzed, and the width between the spikes can be represented by the width between the mean pre-impact velocity and the mean post-impact velocity on the levels, respectively. We verify that the width is inversely proportional to the vibration frequency of the plate. Additionally, it is demonstrated that the probability density functions of pre-impact velocity and post-impact velocity are described by the Gaussian distribution.