Effect of Impact Vibration Absorber with Hysteresis Damping

An analytical method is proposed for the random response of the primary mass with an impact damper having hysteresis damping. The impact damper is one of the dynamic vibration absorbers in which motion of auxiliary mass is limited by motion limiting stop or placed inside a container. In actual collision phenomena, the energy loss in a collision and duration of collision are not negligible small. Then, hysteresis loop characteristics is introduced. In this paper, considering above mentioned points, an analytical model with hysteresis damping is introduced. The mean square response of the primary mass is obtained from the moment equations introducing the equivalent linearization method. As earthquake excitations, nonstationary filtered white noise, product of envelope function with respect to time and stationary filtered white noise, are used. Using the proposed method, the random responses of the primary mass with the impact damper are compared with those with the vibration damper (the undamped dynamic vibration absorber). It is concluded that the impact damper having hysteresis damping is more effective for reducing the vibration of primary mass subjected to earthquake excitations.