The elastic vibration of rotationally ring-shaped periodic structure (RRPS) subjected to angular velocities applied about three orthogonal directions are examined. An analytical model having in-plane radial and tangential displacements is developed by using Hamilton's principle. The modeling leads to a partial differential equation with revolution effect, based on which the eigenvalue splitting, mode contamination and vibration instability are examined by focusing on their evolutions with the support count, support strength and revolution speed. The eigensolutions are formulated by perturbation-superposition method. The results imply that the splitting, contamination and instability follow similar rules with those of stationary RRPS, which are heavily affected by the revolution speed. The dependence of parameters on eigensolutions and especially the relationships between eigenvalue splitting and principal instability, and those between mode contamination and combination instability are demonstrated based on a sample RRPS. The principal instability can occur at splitting eigenvalues, and the combination instability can arise in the presence of mode contamination. Main results are compared with the existing ones in the open literature.

研究了绕三个正交方向施加角速度的旋转环形周期性结构（RRPS）的弹性振动。利用汉密尔顿原理建立了具有平面内径向和切向位移的解析模型。该模型导致了具有旋转效应的偏微分方程，在此方程基础上，通过关注支撑数，支撑强度和旋转速度的演变，检验了特征值​​分裂，模式污染和振动不稳定性。本征解是通过摄动叠加法确定的。结果表明，分裂，污染和不稳定性遵循与固定RRPS相似的规则，后者受转速的影响很大。基于样本RRPS，证明了参数对本征解的依赖性，尤其是本征值分裂与主不稳定性之间的关系，以及模式污染与组合不稳定性之间的关系。主不稳定性可能发生在分裂特征值时，并且组合不稳定性可能会在模式污染的情况下出现。将主要结果与公开文献中的现有结果进行比较。