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

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 the 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.