PERIODIC MOTIONS AND ROBUST STABILITY OF THE MULTI-DEGREE-OF-FREEDOM SYSTEMS WITH CLEARANCES
存在间隙的多自由度系统的周期运动及Robust稳定性

An analysis is presented for determining the dynamical responses for a class of multi degree of freedom systems with clearances or gaps. The systems consist of linear components, but the maximum displacement of one of the masses is limited to a threshold value by a rigid wall. The system is uncoupled by using modal matrix approach. Based on the impacting condition and the matching condition according to the impact law, we have derived the periodic motions and their stability conditions. Then, applying the Lyapunov method to the difference equations of disturbances of periodic motions, the conditions for the robust stability of the impact-vibrating systems with uncertain parameters are obtained. The effectiveness of the present approach is demonstrated by applying it to a two degree of freedom system.