A multi-degree-of-freedom vibratory system with a clearance is considered. The system consists of linear components, but the maximum displacement of one of the masses is limited to a threshold value by two symmetrical rigid stops. The system is uncoupled by using modal matrix approach. Based on the impacting condition and the matching condition according to the impact law, double-impact periodic motion and Poincaré mapping of the system are derived analytically. Stability condition of double-impact periodic motion is given, and local bifurcations of the system are analyzed by using Jacobian matrix of impact mapping. The effectiveness of the present approach is demonstrated by applying it to a two-degree- of-freedom system.
Vibration, Clearance, Periodic motion, Stability, Bifurcations
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