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Shock and Vibration
Volume 18 (2011), Issue 1-2, Pages 91-103

The Effects of Crack on the Transmission Matrix of Rotor Systems

Z.K. Peng,1 Z.Q. Lang,2 G. Meng,1 and F.L. Chu3

1State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
2Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK
3Department of Precision Instruments, Tsinghua University, Beijing 100084, China

Received 4 February 2010; Revised 15 April 2010

Copyright © 2011 Hindawi Publishing Corporation. 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.


The dynamic behavior of rotor containing crack is a subject of particular interest and has been extensively investigated by researchers. The effects of crack on the natural frequencies and modal shapes and motion orbits of rotor systems have already been well explored by researchers. In the present study, the infl uence of crack on the transmission matrices of the rotor systems is investigated by using the FEM (finite element method) analysis and the HBM (harmonic balance method) technique. It is for the first time revealed that there are differences between the transmission matrices for the fundamental frequency components and the transmission matrices for the super-harmonic components, and the differences are mainly determined by the crack location. The results are validated by numerical experiments where the system responses of a rotor system are obtained using Runge-Kutta method. The results are of significance for the development of effective crack detection methods in practice.