存在间隙的多自由度系统的周期运动及Robust稳定性

PERIODIC MOTIONS AND ROBUST STABILITY OF THE MULTI-DEGREE-OF-FREEDOM SYSTEMS WITH CLEARANCES

研究一类存在间隙的多自由度振动系统的动态响应．系统由线性元件构成，但其中一个元件的最大位移不能超过由刚性平面约束所确定的阀值．应用模态矩阵方法将系统解耦，并根据碰撞条件和由碰撞规律所确定的衔接条件求得系统的周期运动及其稳定条件．将Ｌｙａｐｕｎｏｖ方法应用于周期运动的扰动差分方程，导出了含不确定参数的碰撞振动系统周期运动的鲁棒（Ｒｏｂｕｓｔ）稳定性条件．

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.