Abstract
In this paper, the floating frame of reference approach is applied to the dynamics of the impact of flexible bodies, while component mode synthesis is used to describe deformation. The influence of the reference conditions, that indicate the type of attachment between the body fixed frame of reference and the flexible bodies, is investigated. Rigid and free attachments allow the use of fixed interface and free interface normal modes, respectively. A finite number of fixed interface modes does not fulfil the natural boundary condition at the attachment point. Free interface normal modes cannot describe the compressive forces at the contact surface. However, it is shown that both set of modes are able to describe the impact-induced elastic waves. In the evaluation of the kinematic coefficient of restitution, these two approaches differ significantly. When free attachment is considered, the derivatives of the reference co-ordinates coincide with the equivalent rigid body velocities of the flexible bodies, remaining constant after the impact. However, if the body frame of reference is rigidly attached, the equivalent rigid body velocities of the flexible body have to be evaluated as a linear combination of the derivative of reference and elastic co-ordinates. The axial impact of a rigid body on a flexible rod and the transverse impact of a flexible pendulum with a fixed stop are simulated to illustrate these facts. Hertzian contact forces are assumed to occur during impact.
