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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 810147, 7 pages
http://dx.doi.org/10.1155/2013/810147
Research Article

Efficient Procedures of Sensitivity Analysis for Structural Vibration Systems with Repeated Frequencies

College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China

Received 19 May 2012; Revised 20 November 2012; Accepted 18 December 2012

Academic Editor: Marco H. Terra

Copyright © 2013 Shijia 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.

Abstract

Derivatives of eigenvectors with respect to structural parameters play an important role in structural design, identification, and optimization. Particularly, calculation of eigenvector sensitivity is considered when the eigenvalues are repeated. A relaxation factor embedded in the combined approximations (CA) method makes it effective to the structural response at various modified designs. The proposed method is feasible after overcoming the defection of irreversibility of the characteristic matrix. Numerical examples show that it is easy to implement the computational procedure, and the method presented in this paper is efficient for the general linear vibration damped systems with repeated frequencies.