Modeling and Stability Analysis of a Flexible Rotor Based on the Timoshenko Beam Theory

Based on the Timoshenko beam theory, a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton's principle and Euler angles. The associated conventional model is provided for comparison purpose. The features of the proposed mathematical model are discussed based on some selected coordinate systems. The frequencies and modes are investigated to show the influences of centrifugal terms on the stability of the gyroscopic systems. The results show that the novel model proposed may lose stability due to the centrifugal terms. It is also found that the backward precession mode can be changed into a forward one beyond the critical rotating velocity.