Smooth vs. pieced-interval dynamic modeling of impulsive events in multibody mechanical systems

Impulsive responses often arise in mechanical systems due to collision, impact, joint clearances, machine tool interaction, and material handling processes. Impulsive events take place during very short-lived intervals, and are normally associated with redistribution of momentum. The redistribution of momentum may take place instantaneously or during a very short interval, thus giving rise to discontinuities in the system's velocities. In this context, two modeling approaches are presented. The first approach adopts a smooth representation over the shortlived interval. In this case, the impulsive event is modeled while taking into consideration the mechanics of the contacting bodies. The second is a discontinuous dynamic model, in which the impulsive event is assumed to take place at an instant of time. The corresponding instantaneous redistribution of momentum results in jump discontinuities in the system's velocities, which are calculated to update the system state vector for starting the next interval. The merits of the two modeling approaches are stated in the light of numerical simulations.