中文摘要：

针对工程领域广泛存在的一类分组旋转周期结构开展了解析动力学研究.提出了一种利用等效对称单元判别固有频率是否分裂的简便方法.采用直接摄动法研究了对称单元分布对模态特性的影响,揭示了等效对称子单元的分组方式与固有频率分裂之间的映射关系.该映射关系提供了一种抑制固有频率分裂的对称单元拓扑调整方法.该方法可用于超声电机和陀螺仪等对固有频率分裂敏感的重要领域.仿真结果验证了固有频率分裂规律的正确性.

英文摘要：

The rotationally periodic structure with grouped features can be found in numerous engineering applica- tions. The dynamic characteristic of this kind of structure was analytically investigated. A new concept of equivalent feature was introduced, which could be used to predict the frequency splitting behavior of the structure. The effect of the feature topology on the modal properties was examined by using the direct perturbation method. And the relation- ships between the topology of the sub-feature and the natural frequency splitting were obtained, which presented a simple rule goveming the elimination of the frequency splitting. The main results could be applied to some important engineering applications such as the ultrasonic motors and vibratory gyroscopes heavily affected by the natural fre- quency splitting. The splitting behaviors were verified by the simulation results.