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Shock and Vibration
Volume 2016 (2016), Article ID 8194549, 8 pages
Research Article

Structural Damage Detection by Using Single Natural Frequency and the Corresponding Mode Shape

State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China

Received 17 August 2015; Revised 29 October 2015; Accepted 16 November 2015

Academic Editor: Juan P. Amezquita-Sanchez

Copyright © 2016 Bo Zhao et al. 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.


Damage can be identified using generalized flexibility matrix based methods, by using the first natural frequency and the corresponding mode shape. However, the first mode is not always appropriate to be used in damage detection. The contact interface of rod-fastened-rotor may be partially separated under bending moment which decreases the flexural stiffness of the rotor. The bending moment on the interface varies as rotating speed changes, so that the first- and second-modal parameters obtained are corresponding to different damage scenarios. In this paper, a structural damage detection method requiring single nonfirst mode is proposed. Firstly, the system is updated via restricting the first few mode shapes. The mass matrix, stiffness matrix, and modal parameters of the updated system are derived. Then, the generalized flexibility matrix of the updated system is obtained, and its changes and sensitivity to damage are derived. The changes and sensitivity are used to calculate the location and severity of damage. Finally, this method is tested through numerical means on a cantilever beam and a rod-fastened-rotor with different damage scenarios when only the second mode is available. The results indicate that the proposed method can effectively identify single, double, and multiple damage using single nonfirst mode.