Effect of Gravity on the Performance of an Impact Damper: Part 1. Steady-State Motion

Abstract

This paper, which examines the effect of gravity on the performance of an impact der, extends a previous paper (I)‡ concerned with the horizontal system. The analysis is in two parts: Part 1 which concerns itself with the calculation of all the theoretically possible steady-state motions with two impacts of the free mass, one at each end of its container, per cycle of the main mass; and Part 2§ which examines the dynamic stability and kinematic viability of the various steady-state solutions obtained in Part 1. The impact damper consists of a small mass free to move within a rigid container attached to the main vibrating system. Vibration suppression is achieved through energy dissipation during impacts and through cancellation of the effect of the external exciting force by the cyclical reaction of the free mass on the main system. The analysis shows that, in general, several different steady-state motions are theoretically possible for a given exciting frequency and that the effect of gravity on the motion of the system is to reduce the frequency range of two-impact-per-cycle motion. It is also shown that under the practically important condition of resonance the motion consists of two impacts of the free mass per cycle of the main mass. Outside the resonant condition, where the motion of the main mass is weak, the free mass may impact more or less than twice per cycle. This condition is not studied.