中文摘要：

针对旋转环状周期结构的参激振动问题,在惯性坐标系下采用能量法建立了时变弹性动力学模型.为了获得系统的动力稳定性,采用坐标变换方法消除了该模型的时变性,然后根据经典振动理论得到了系统的特征值.根据该特征值分析了模态特性和不稳定性.结果表明：在旋转支撑作用下,系统的固有频率发生分裂;对于某些转速,系统表现出发散或颤振不稳定.此外,利用 Floquét 理论计算了系统的不稳定域和动态响应,并将其与解析预测进行对比.该研究有助于快速分析该类参激系统的动力稳定性,并获得指导工程实践的解析结果.

英文摘要：

This work aims at the parametric vibration of rotational ring-shaped periodic structures. An elastic model of the structure is developed by using energy method in the inertial coordinate,and the eigenvalues are obtained by using general vibration theory after the coordinate transformation. The modal characteristics and the unstable bounda-ries are identified by the eigenvalues. The results show that natural frequency splittingcan occur due to the effect of rotating supports,and there exist divergence and flutter instabilities at certain rotating speed. Besides,the unstable regions and the dynamic response are obtained by using the Floquét theory for the verification on analytical estima-tions. The research contributes to the optimization of the analysis of dynamic instability for similar structures,and the analytical results are obtained to guide the practice in engineering.