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 damper, extends a previous paper (I)$ concerned with the horizontal system. T h e 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 s 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.T h e 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. I N T R O D U C T I O NTHE impact damper consists of a small loose mass which rattles inside a container attached to the vibrating system. Repetitive impacts of the free mass against the ends of the container have the effect of attenuating the motion of the main system. This is achieved partly through the loss of kinetic energy on impact and partly through the phasing and magnitude of the fundamental Fourier component of the cyclical impulsive forces with respect to the external exciting force. The device is, in effect, a vibration absorber in the sense that an auxiliary system is fixed to the main system in order to suppress a resonance but differs from the conventional tuned vibration absorber because the free mass has an indeterminate natural frequency of oscillation within the container. The device is most effective when the dominant Fourier component of the impulsive forces has the same frequency as the external exciting force, that is, when there is one impact at each end of the container during each cycle of the main system. It is this condition which is treated in the present analysis.The M S . of this paper was received at the Institution on 13th November 1969 and accepted for publication on 5th M a y 1970. 44

The Effectiveness of the Impact Damper with a Spring-Supported Auxiliary Mass

“…9 together with that previously determined experimentally (13). The predicted curve coincides with that predicted by the previous theory developed by Sadek (7).…”

Relaxation of a spring with an attached granular damper

“…We will show that this behavior may be attributed to different collective modes of dynamics of granular matter in an oscillating box. For our investigation we wish to exclude the influence of gravity on the dynamics of excited granular matter and, thus, on granular damping [21,[31][32][33][34][35][36]. Therefore, we refer to recent experiments on granular damping under conditions of microgravity [37].…”

Particle impact dampers: Past, present, and future

“…For example, Sadek et al [136,137] studied the influence of gravity on the impact damper and found that the damper has better effect in zero gravity environment. Moreover, in the vicinity of resonance, asymmetric collisions twice per cycle are dominant.…”