Whirling and Stability Analyses of FG-rotors with Variable Diameter Subjected to Axial Load and Torsional Torque

In this paper, whirling and stability analyses of a rotor made of functionally graded materials are investigated. The rotor is modeled based on Timoshenko beam theory and gyroscopic effects are considered. Diameter and mechanical properties of the rotor are considered to be variable in longitudinal direction and the rotor is considered to be subjected to axial load and torsional torque. In order to generalization of the modeling of bearings, each of them is replaced with foursprings; two translational and two rotational acting on two perpendicular directions. Using Newton’s second law, the set of governing equations and external boundary conditions are derived and solved numerically using differential quadrature method (DQM). Convergence and accuracy of the presented solution are confirmed and effect of various parameters including power index, angular velocity ofspin, value and sign of applied axial load and torsional torque on the forward and backward frequencies and stability of the rotor are investigated. Numerical results show that all forward and backward frequencies and therefore critical speeds decrease by increase in power law, applying axial pressure load and torsional torque and increase by applying axial tension force.