On the gyroscopic and centrifugal effects in the free vibration of rotating beams

This paper addresses the gyroscopic and centrifugal effects on vibrations of rotating Bernoulli–Euler beams. The gyroscopically coupled system is established as a complex eigenvalue problem. It is concluded that there exist three types of velocity-dependent terms that contribute to the natural frequencies with different effects. In particular, the contribution of gyroscopic terms and static and dynamic centrifugal terms to the natural frequencies are discussed for free vibrations of rotating beams with constant angular velocity. On the other hand, the vibrations in different directions coupled through the gyroscopic terms are investigated. Some numerical examples for the elliptic vibration modes in the rotating plane are presented and the results reveal the actual vibration contour of the rotating beams.