Numerical Model of Impact-Damped Continuous Systems

Abstract

In earlier studies of multiple-degree-of-freedom (MDOF) systems, an impact had always been assumed to affect the velocity of the lumped mass at the point of impact. Experiments show that the velocities of all points in a continuous system are influenced by the impact of the damper. In this study, the steady-state behavior of an impact-damped beam is modeled by applying conservation of momentum between the impact damper and the modal masses of the beam. Friction and gravity are considered for the case of horizontal and vertical motions, respectively. The impact damper exhibits a wide range of impact patterns and its optimum behavior occurs at two impacts per cycle. Three types of impact are identified for the case of two impacts per cycle, one of which expands the limit cycle of the system and therefore is detrimental. Within limits, the effectiveness of the impact damper improves with an increase in its mass, with a decrease in the coefficient of restitution, and when it is at a point of large amplitude. An optimum gap exists for each of the first three modes of vibrations. The damper expands the limit cycle of the system at higher excitation amplitudes. The phenomena of bouncedown and stuck impacts are shown to exist in continuous systems.