Dynamics and performance of a vertical impact damper

Particle impact dampers (PIDs) provide effective vibration damping in numerous applications. However, our theoretical understanding of the behavior of such dampers is incomplete, and limits their use. As a PID can be considered to be a more general version of an impact damper, predicting the performance of an impact damper is an essential step towards being able to predict the behavior of PIDs. This research seeks to understand the dynamics of an impact damper as well as those parameters which govern its behavior. The system considered is an impact damper with a ceiling, harmonically excited in the vertical direction under the influence of gravity. A difference equation approach is used wherein the variables at one impact uniquely dictate the variables at the next impact, leading to a two-dimensional map. This map is then solved using numerical iteration, given an initial condition. Periodic and irregular impact motions are observed. The dependence of the effective damping loss factor, as well the nature of the response, on parameters such as gap clearance, coefficient of restitution, and base acceleration is addressed. The loss factor results indicate peak damping for certain combinations of parameters. These combinations correspond to a region in parameter space in which two-impact-per-cycle motions are observed over a wide range of non-dimensional base accelerations. The value of the non-dimensional acceleration at which the onset of two-impact-per-cycle solutions occurs depends on the non-dimensional gap clearance and the coefficient of restitution. The range of non-dimensional gap clearances over which two-impact-per-cycle solutions are observed increases as the coefficient of restitution increases. Symmetrical two-impact-per-cycle solutions are possible only in the limit of infinite non-dimensional base acceleration. In the regime of two-impact-per-cycle solutions, the value of the non-dimensional base acceleration corresponding to the onset of these solutions initially decreases and then increases with increasing non-dimensional gap clearance. Because the two-impact-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer. Design curves are generated which indicate the kind of steady state motion observed and the associated loss factor as a function of the non-dimensional gap clearance and the coefficient of restitution. These non-dimensional parameters can be appropriately chosen using the design curves so as to yield two-impact-per-cycle solutions.