Inner mass impact damper for attenuating structure vibration

The behaviors of a vibration system suppressed with an impact damper are investigated, where the impact damper is simplified as a combination of spring and viscous damping. The analytical theory for the optimal impact control algorithms for impact damper is developed, and the accurate expressions are derived for the optimal values of the impact damper damping and initial displacement in a single-degree-of-freedom structure. The relation between coefficient of restitution and impact damping ratio is obtained. The investigation shows that the effective reduction of the vibration response is nearly independent of the number of impacts, but primarily related to the type of collision which the impact mass collides with the main mass face-to-face. This theory is generalized to continuous structures. An example of an impact damper in a rotating cantilever beam demonstrates that the impact dampers are suitable for attenuating the impulse response of structures unconditional stable without the requirement of the accuracy of the modal information.