An impact model of a ball bouncing on a flexible beam

In this work we investigate a model for the description of the impact of a ball with a flexible beam. The coupling of the kinematic parameters of the ball (the velocity components) with the vibration modes of the beam are taken into account by using the Hertz theory of impact. We solve the model equations numerically in a few physically relevant cases and illustrate the variation of the modal coefficients of the beam and of the velocity components of the ball during the impact. The restitution coefficient, the size of the deformation region and the impact duration are also reported as functions of the impact velocity and of the impact location.