Whirling analysis of non-uniform Timoshenko rotors subjected to axial load and torsional torque

چکیده مقاله

In this paper, Generalized Differential Quadrature Method (GDQM) is used to analyze free whirling of non-uniform rotors subjected to axial load and torsional torque. Timoshenko beam theory is used to investigate gyroscopic effect. Also, bearings at two ends of the rotor are replaced by four springs; two translational and two rotational, acting on two perpendicular directions. First, using Hamilton's principle, set of governing equations and external boundary conditions are derived. Then, these equations are formulated and solved using differential quadrature rules. Next, accuracy of the proposed method is confirmed by comparison of numerical results with available exact solutions. Finally, effects of angular velocity of spin, the applied axial load and torque on forward and backward frequencies are investigated. The most advantages of the proposed method are its usability for any variation in diameter of the rotor and being less time-consuming in comparison with other presented methods.