Dissipative properties for a ball bouncing on a vertically vibrating plate

Abstract

The collision characteristics of a ball impacting on a vertically vibrating plate are different from those normally presented in the ball-ball or ball-plate collision, because the vibration of the plate inevitably gets involved in the collision process. We experimentally study the behavior of a steel ball bouncing on a vertically vibrating plate, and determine the dependence of the coefficient of restitution and the collision duration on the impact velocity. In the experiment, a double-layer composite structural plate is used, which is formed by gluing a piece of polyethylene onto a stainless steel sheet. It is found that the vibration of the plate makes the coefficient of restitution to be no longer a single-valued function of the impact velocity, but rather multi-valued, and exhibit a complex but regular dispersion structure. To account for such dispersion structure, a collision dynamics model is developed in which the inertial force due to the vibration of the plate is included. The energy loss caused by viscous deformation and inertial force is analyzed. Both the coefficient of restitution and the collision duration calculated by this model agree well with the experimental ones.