中文摘要：

为揭示环状旋转周期结构的模态特性,以含附加结构的薄圆环为研究对象,采用直接模态摄动法建立了该周期结构动力特性近似解析方法,获得了环状旋转周期结构的模态表达式.给出了由附加结构的个数及振型的波数决定的固有频率分裂条件以及标准圆环振型与摄动振型之间的调制规律.研究表明：分裂的频率中余弦项频率值改变,而正弦项频率值保持不变;重根对应的振型被摄动振型的正、余弦项谐波调制,分裂根对应的振型仅余弦项振型被调制,且重根振型的调制程度大于分裂根振型.仿真结果证明了解析结论的正确性.

英文摘要：

By taking a thin ring with additional structures as the research object,the approximate analytical method of dynamic characteristics and modal expressions of annular rotationally periodic structures were established by using direct modal perturbation method to reveal the modal characteristics of such structures.Natural frequency splitting conditions were defined by the number of additional structures and wave number,and the modulated rules between standard annular mode shape and perturbation mode shape were presented.The conclusions show that the cosine item of the splitting doublet changes,while its sine item keeps invariant.Mode shape corresponding to the repeated doublet is modulated by sine and cosine harmonics of perturbation mode shape.Mode shape corresponding to splitting doublet is merely modulated by cosine harmonics.And the modulated degree of repeated doublet is greater than splitting doublet.Simulation results are well consistent with the analytical conclusions.