A note on coefficient of restitution models including the effects of impact induced vibration

In this work multi-modal systems subject to impact are considered. Using energy balance techniques for an arbitrary contact interval the effects of modal vibration can be included. The energy balance is used to obtain a relationship between the coefficient of restitution and the modal energy during the contact period. This allows the effects of impact induced vibration to be considered. The subsequent analytical relationships demonstrate that increasing contact duration and excitation of higher modes can reduce the effective value of the coefficient of restitution. It is also shown how this approach can be related to work on energetically consistent impacts.