Free whirling analysis of multi-step Timoshenko rotor with multiple bearing using DQEM

In this paper, differential quadrature element method (DQEM) is used to analyze the free transverse vibration of multi-stepped rotors resting on multiple bearings. Timoshenko beam theory is used to show the gyroscopic effects; Also each bearing is replaced with four springs; two translational and two rotational acting on two perpendicular directions. Governing equations, compatibility conditions at the each step and each bearing and external boundary conditions are derived and formulated by the differential quadrature rules. First, convergence and versatility of the proposed method are tested by the presented exact solutions. Then, the Campbell diagram is derived for a desired case study and variation of natural frequencies is investigated versus angular velocity of spin. The most advantage of the proposed method is being less time-consuming in comparison with the other methods, especially for cases with high number of steps and bearings. Accuracy of the proposed method is confirmed by the presented exact solutions and effect of angular velocity of spin on natural frequencies (Campbell diagram) is investigated. Comparison of the proposed method with the exact solutions revealed the convergence and accuracy of the proposed method.