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Mathematical Problems in Engineering
Volume 2014, Article ID 896261, 6 pages
Research Article

Structural Dynamics Model Updating with Positive Definiteness and No Spillover

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received 21 February 2014; Revised 16 May 2014; Accepted 22 May 2014; Published 3 June 2014

Academic Editor: Mohammad I. Younis

Copyright © 2014 Yongxin Yuan. 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.


Model updating is a common method to improve the correlation between structural dynamics models and measured data. In conducting the updating, it is desirable to match only the measured spectral data without tampering with the other unmeasured and unknown eigeninformation in the original model (if so, the model is said to be updated with no spillover) and to maintain the positive definiteness of the coefficient matrices. In this paper, an efficient numerical method for updating mass and stiffness matrices simultaneously is presented. The method first updates the modal frequencies. Then, a method is presented to construct a transformation matrix and this matrix is used to correct the analytical eigenvectors so that the updated model is compatible with the measurement of the eigenvectors. The method can preserve both no spillover and the symmetric positive definiteness of the mass and stiffness matrices. The method is computationally efficient as neither iteration nor numerical optimization is required. The numerical example shows that the presented method is quite accurate and efficient.