Impact of a ball with a flexible beam

Abstract

The impact of a ball with a flexible beam is analysed both experimentally and theoretically. The impact generates a bending wave that may or may not return to the impact point before the ball bounces off the beam. If the ball rebounds before the bending wave returns, then the rebound speed of the ball is determined by localised bending of the beam in the vicinity of the impact point. For a short duration impact, the rebound speed is therefore independent of whether the beam is freely supported or clamped at one or both ends, unless the impact occurs close to an end of the beam. Two different values of the coefficient of restitution can be defined, depending on whether the speed of the beam is measured when the ball rebounds or at a later stage. Experimental results were obtained using a small rubber ball impacting light wood and steel beams. A video camera and two piezoelectric disks were used to capture the relevant ball speeds and vibration response of the beam. The experiment would be suitable for undergraduate students.