E ects of Rotary Inertia and Gyroscopic Momentum on the Flexural Vibration of Rotating Shafts Using Hybrid Modeling


Department of Mechanical Engineering,Ferdowsi University of Mashhad


Abstract. In this paper, the e ect of shaft rotation on its natural frequency is investigated.
Considering rotary inertia and gyroscopic momentum, the fourth order di erential equation representing
exural vibration of the shaft is solved by the new analytical method. The Distributed Lumped Modeling
Technique (DLMT) is applied to obtain the transfer matrix for the distributed elements using the proposed
method and for the lumped elements consisting of rotary inertia and gyroscopic e ects. The results
obtained by this method are compared and veri ed with the results of two other methods. The e ects of
shaft diameter, shaft length and disk inertia on the natural frequency are discussed for various speeds. It
is shown that, while the new method brings highly accurate results, its simplicity and accuracy provide
proper application for use in industrial systems.