In this paper, primary resonances of a flexible rotor suspended by active magnetic bearings are investigated. The rotor has large amplitude vibrations, which leads to nonlinearities in curvature and inertia. In addition, nonlinearity characteristics of active magnetic bearings are considered. In modeling of the shaft, rotary inertia and shear deformation are neglected but gyroscopic effect is included. Here, the equations of motion and related boundary conditions are both nonlinear. To analyze the dynamical behavior of the system, the renormalization group method is directly applied to the partial differential equations of motion and boundary conditions. The effects of different parameters of the shaft and active magnetic bearings on the frequency response of the system in the neighborhood of critical speeds are investigated, and it is shown that both hardening and softening nonlinearity behaviors are possible.

中文翻译：

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主动电磁轴承支承的非线性柔性轴的初共振分析。

在本文中，研究了由主动磁轴承悬挂的挠性转子的初级共振。转子具有较大的振幅振动，这会导致曲率和惯性非线性。另外，考虑了有源电磁轴承的非线性特性。在轴的建模中，忽略了旋转惯性和剪切变形，但包括了陀螺效应。在这里，运动方程和相关的边界条件都是非线性的。为了分析系统的动力学行为，将重归一化组方法直接应用于运动和边界条件的偏微分方程。研究了轴和有源电磁轴承的不同参数在临界转速附近对系统频率响应的影响，