王世宇^1,2, 孙文嘉¹, 夏营¹, 修杰³
AuthorsHTML:王世宇^1,2, 孙文嘉¹, 夏营¹, 修杰³
AuthorsListE:Wang Shiyu^1,2, Sun Wenjia¹, Xia Ying¹, Xiu Jie³
AuthorsHTMLE:Wang Shiyu^1,2, Sun Wenjia¹, Xia Ying¹, Xiu Jie³
Unit:1. 天津大学机械工程学院，天津 300354；2. 天津市非线性动力学与控制重点实验室，天津 300354；3. 天津大学电气自动化与信息工程学院，天津 300072
Unit_EngLish:1. School of Mechanical Engineering, Tianjin University, Tianjin 300354, China
2．Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin 300354, China
3．School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
Abstract_Chinese: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．
Abstract_English: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 boundaries are identified by the eigenvalues. The results show that natural frequency splitting can 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 estimations. 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.
Keyword_Chinese:环状周期结构; 坐标变换; 特征值; 不稳定性预测
Keywords_English:ring-shaped periodic structure; coordinate transformation; eigenvalues; instability prediction

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