Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30309
An Efficient Iterative Updating Method for Damped Structural Systems

Authors: Jiashang Jiang


Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

Keywords: Model Updating, iterative algorithm, Optimal approximation, damped structural system

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 957


[1] M. Baruch, I. Y. Bar-Itzhack, Optimal weighted orthogonalization of measured modes, AIAA Journal 16 (1978) 346–351.
[2] A. Berman, E. J. Nagy, Improvement of a large analytical model using test data, AIAA Journal 21 (1983) 1168–1173.
[3] F. S. Wei, Mass and stiffness interaction effects in analytical model modification, AIAA Journal 28 (1990) 1686–1688.
[4] Y. B. Yang, Y. J. Chen, A new direct method for updating structural models based on measured modal data, Engineering Structures 31 (2009) 32–42.
[5] Y. Yuan, A model updating method for undamped structural systems, Journal of Computational and Applied Mathematics 219 (2008) 294–301.
[6] M. I. Friswell, J. E. Mottershead, Finite Element Moodel Updating in Structural Dynamics, Dordrecht: Klumer Academic Publishers, 1995.
[7] M. I. Friswell, D. J. Inman, D. F. Pilkey, The direct updating of damping and stiffness matrices, AIAA Journal 36 (1998) 491–493.
[8] Y. C. Kuo, W. W. Lin, S. F. Xu, New methods for finite element moodel updating problems, AIAA Journal 44 (2006) 1310–1316.
[9] D. L. Chu, M. Chu, W. W. Lin, Quadratic model updating with symmetry, positive definiteness, and no spill-over, SIAM Journal on Matrix Analysis And Applications 31 (2009) 546–564.
[10] Y. Yuan, H. Dai, On a class of inverse quadratic eigenvalue problem, Journal of Computational and Applied Mathematics 235 (2011) 2662–2669.
[11] F. Ding, T. Chen, Iterative least squares solutions of coupled Sylvester matrix equations, Systems & Control Letters 54 (2005) 95–107.
[12] F. Ding, P. X. Liu, J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Applied Mathematics and Computation 197 (2008) 41–50.
[13] A. Ben-Israel, T. N. E. Greville, Generalized Inverses: Theory and Applications (second ed), New York: Springer, 2003.