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.
[1] M. Baruch, I. Y. Bar-Itzhack, Optimal weighted orthogonalization of
measured modes, AIAA Journal. 16 (1978) 345-351.
[2] M. Baruch, Optimization procedure to correct stiffness and flexibility
matrices using vibration tests, AIAA Journal. 16 (1978) 1208-1210.
[3] J. G. Beliveau, Identification of viscous damping in structures from
modal information, ASME Journal of Applied Mechanics. 43(1976) 335-
338.
[4] A. Ben-Israel, T. N. E. Greville, Generalized Inverse: Theory and
Applications, Wiley, New York, 1974.
[5] A. Berman, Comment on "Optimal weighted orthogonalization of measured
modes", AIAA Journal. 1979, 17 (1979) 927-928.
[6] A. Berman, E. J. Nagy, Improvement of a large analytical model using
test data, AIAA Journal. 21 (1983) 1168-1173.
[7] 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.
[8] M. I. Friswell, D. J. Inman, D. F. Pilkey, The direct updating of damping
and stiffness matrices, AIAA Journal. 36 (1998) 491-493.
[9] S. R. Ibrahim, Dynamic modeling of structures from measured complex
modes, AIAA Journal. 21 (1983) 898-901.
[10] C. Minas, D. J. Inman, Identification of a nonproportional damping
matrix from incomplete modal information, Journal of Vibration and
Acoustics. 113 (1991) 219-224.
[11] 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.
[12] F. Tisseur, K. Meerbergen, The quadratic eigenvalue problem, SIAM
Review. 43 (2001) 235-286.
[13] F.-S. Wei, Stiffness matrix correction from incomplete test data, AIAA
Journal. 18 (1980) 1274-1275.
[14] F.-S. Wei, Mass and stiffness interaction effects in analytical model
modification, AIAA Journal. 28 (1990) 1686-1688.
[15] F.-S. Wei, Structural Dynamic model improvement using vibration test
data, AIAA Journal. 28 (1990) 175-177.
[16] 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.
[1] M. Baruch, I. Y. Bar-Itzhack, Optimal weighted orthogonalization of
measured modes, AIAA Journal. 16 (1978) 345-351.
[2] M. Baruch, Optimization procedure to correct stiffness and flexibility
matrices using vibration tests, AIAA Journal. 16 (1978) 1208-1210.
[3] J. G. Beliveau, Identification of viscous damping in structures from
modal information, ASME Journal of Applied Mechanics. 43(1976) 335-
338.
[4] A. Ben-Israel, T. N. E. Greville, Generalized Inverse: Theory and
Applications, Wiley, New York, 1974.
[5] A. Berman, Comment on "Optimal weighted orthogonalization of measured
modes", AIAA Journal. 1979, 17 (1979) 927-928.
[6] A. Berman, E. J. Nagy, Improvement of a large analytical model using
test data, AIAA Journal. 21 (1983) 1168-1173.
[7] 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.
[8] M. I. Friswell, D. J. Inman, D. F. Pilkey, The direct updating of damping
and stiffness matrices, AIAA Journal. 36 (1998) 491-493.
[9] S. R. Ibrahim, Dynamic modeling of structures from measured complex
modes, AIAA Journal. 21 (1983) 898-901.
[10] C. Minas, D. J. Inman, Identification of a nonproportional damping
matrix from incomplete modal information, Journal of Vibration and
Acoustics. 113 (1991) 219-224.
[11] 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.
[12] F. Tisseur, K. Meerbergen, The quadratic eigenvalue problem, SIAM
Review. 43 (2001) 235-286.
[13] F.-S. Wei, Stiffness matrix correction from incomplete test data, AIAA
Journal. 18 (1980) 1274-1275.
[14] F.-S. Wei, Mass and stiffness interaction effects in analytical model
modification, AIAA Journal. 28 (1990) 1686-1688.
[15] F.-S. Wei, Structural Dynamic model improvement using vibration test
data, AIAA Journal. 28 (1990) 175-177.
[16] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59110", author = "Jiashang Jiang and Yongxin Yuan", title = "The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data", abstract = "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.
", keywords = "Model updating, damped gyroscopic system, partially prescribed spectral information.", volume = "5", number = "7", pages = "1021-4", }
