The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data
In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074505Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1447
 M. Baruch, I. Y. Bar-Itzhack, Optimal weighted orthogonalization of measured modes, AIAA Journal. 16 (1978) 345-351.
 M. Baruch, Optimization procedure to correct stiffness and flexibility matrices using vibration tests, AIAA Journal. 16 (1978) 1208-1210.
 J. G. Beliveau, Identification of viscous damping in structures from modal information, ASME Journal of Applied Mechanics. 43(1976) 335- 338.
 A. Ben-Israel, T. N. E. Greville, Generalized Inverse: Theory and Applications, Wiley, New York, 1974.
 A. Berman, Comment on "Optimal weighted orthogonalization of measured modes", AIAA Journal. 1979, 17 (1979) 927-928.
 A. Berman, E. J. Nagy, Improvement of a large analytical model using test data, AIAA Journal. 21 (1983) 1168-1173.
 B. N. Datta, D. R. Sarkissian, Feedback control in distributed parameter gyroscopic systems: a solution of the partial eigenvalue assignment problem, Mechanical Systems and signal Processing. 16 (2002) 3-17.
 M. I. Friswell, D. J. Inman, D. F. Pilkey, The direct updating of damping and stiffness matrices, AIAA Journal. 36 (1998) 491-493.
 S. R. Ibrahim, Dynamic modeling of structures from measured complex modes, AIAA Journal. 21 (1983) 898-901.
 C. Minas, D. J. Inman, Identification of a nonproportional damping matrix from incomplete modal information, Journal of Vibration and Acoustics. 113 (1991) 219-224.
 D. R. Sarkissian,Theory and computations of partial eigenvalue and eigenstructure assignment problems in matrix second-order and distributed- parameter systems, Ph. D. thesis, Department of Mathematical Science, Northern Illinois University, 2001.
 F. Tisseur, K. Meerbergen, The quadratic eigenvalue problem, SIAM Review. 43 (2001) 235-286.
 F.-S. Wei, Stiffness matrix correction from incomplete test data, AIAA Journal. 18 (1980) 1274-1275.
 F.-S. Wei, Mass and stiffness interaction effects in analytical model modification, AIAA Journal. 28 (1990) 1686-1688.
 F.-S. Wei, Structural Dynamic model improvement using vibration test data, AIAA Journal. 28 (1990) 175-177.
 Z. C. Zheng, G. X. Ren, W. J. Wang, A reduction method for large scale unsymmetric eigenvalue problems in structural dynamics, Journal of Sound and Vibration. 199 (1999) 253-268.