Multi-time scale simulation for impact systems: from wave propagation to rigid-body motion

 Impact response encompasses a variety of complicated dynamic effects including wave propagation, structural vibrations and rigid-body motion. For efficient simulation of impact response with sufficient accuracy, the methods of wave propagation and multibody systems should be combined. This paper deals with an adaptive simulation of impact response during the transition from wave propagation to rigid-body motion. For modeling structural vibrations, the approach of flexible multibody systems with floating frame of reference formulation is used and the impact-induced elastic deformations are assumed to be small. In the simulation of transient impact response, contributions of the elastic coordinates are monitored with regard to their response bounds. When response bounds are reached, the corresponding elastic coordinates are deleted. As a consequence, the number of degrees of freedom of the flexible system is reduced and the efficiency of the simulation improved. Due to material damping, the impact-induced structural vibrations decay and only the rigid-body motion remains. This adaptive simulation approach is experimentally validated for the longitudinal impact of a rigid body against an elastic rod.