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Mathematical Problems in Engineering
Volume 2014, Article ID 325434, 14 pages
Research Article

Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

Department of Mechanical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Republic of Korea

Received 1 January 2014; Accepted 26 March 2014; Published 28 April 2014

Academic Editor: Shueei M. Lin

Copyright © 2014 Sangkyu Choi and Usik Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.