The derivatives of repeated eigenvalues and their associated eigenvectors

Journal of Vibration and Acoustics, Transactions of the ASME

Volumn 118, Issue 3, 1996, Pages 390-397

  Friswell, M I ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; FUNCTIONS; NATURAL FREQUENCIES; NUMERICAL METHODS; OPTIMIZATION; SENSITIVITY ANALYSIS; STIFFNESS MATRIX;

CONTINUITY; DISCONTINUITY; EIGENVALUE AND EIGENVECTOR DERIVATIVES; NELSON METHOD; TAYLOR SERIES;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0030197132     PISSN: 10489002     EISSN: 15288927     Source Type: Journal    
DOI: 10.1115/1.2888195     Document Type: Article

References (19)

1. Mottershead, J. E., and Friswell, M. I., 1993, “Model Updating in Structural Dynamics: A Survey,” Journal of Sound and Vibration, Vol. 167, No. 2, pp. 347-375.
2. Adelman, H. M., and Haftka, R. T., 1986, “SensitMty Analysis of Discrete Structural Systems,” AIAA Journal, Vol. 24, No. 5, pp. 823-832.
3. Fox, R. L., and Kapoor, M. P., 1968, “Rates of Change of Eigenvalues and Eigenvectors,” AIAA Journal, Vol. 6, No. 12, pp. 2426-2429.
4. Lallement, G., and Kosanek, J., 1993, “Parametric Correction of Self Adjoint Finite Element Models in the Presence of Multiple Eigenvalues,” Proceedings of Modern Practice in Stress and Vibration Analysis, Sheffield, England, April, 593-603.
5. Juang, J.-N., Ghaemmaghami, P., and Lira, K. B., 1989, “Eigenvalue and Eigenvector Derivatives of a Nondefective Matrix,” Journal of Guidance, Control, and Dynamics, Vol. 12, No. 4, pp. 480-486.
6. Bernard, M. L., and Bronowicki, A. J., 1994, “Modal Expansion Method for EigensensitMty with Repeated Roots,” AIAA Journal, Vol. 32, No. 7, pp. 1500-1506.
7. Akgtlin, M. A., 1994, “New Family of Modal Methods for Calculating Eigenvector Derivatives,” AIAA Journal, Vol. 32, No. 2, pp. 379-386.
8. Lim, K. B., Juang, J.-N., and Ghaemmaghami, P., 1989, “Eigenvector Derivatives of Repeated Eigenvalues using Singular Value Decomposition,” Journal of Guidance, Control, and Dynamics, Vol. 12, No. 2, pp. 282-283.
9. Nelson, R. B., 1976, “Simplified Calculation of Eigenvector Derivatives,” AIAA Journal, Vol. 14, pp. 1201-1205.
10. Ojalvo, I. U., 1987, “Efficient Computation of Mode-Shape Derivatives for Large Dynamic Systems,” AIAA Journal, Vol. 25, No. 10, pp. 1386-1390.
11. Mills-Curran, W. C, 1988, “Calculation of Eigenvector Derivatives for Stractures with Repeated Eigenvalues,” AIAA Journal, Vol. 26, No. 7, pp. 867-871.
12. Mills-Curran, W. C, 1990, “Comment on Eigenvector Derivatives with Repeated Eigenvalues,” AIAA Journal, Vol. 28, No. 10, pp. 1846.
13. Dailey, R. L., 1989, “Eigenvector Derivatives with Repeated Eigenvalues,” AIAA Journal, Vol. 27, No. 4, pp. 486-491.
14. Wilkinson, J., 1965, The Algebraic Eigenvalue Problem, Oxford University Press.
15. Haftka, R. T., GUrdal, Z., and Kamat, M. P., 1990, Elements of Structural Optimisation, Second Edition, Kluwer Academic Publishers.
16. Hou, G. J. W., and Kenny, S. P., 1992, “Eigenvalue and Eigenvector Approximate Analysis for Repeated Eigenvalue Problems,” AIAA Journal, Vol. 30, No. 9, pp. 2317-2324.
17. PeSek, L., 1994, “The Updating of Mechanical Models with Repeated Eigenvalues by the Inverse SensitMty Method,” Proceedings of the 19th International Seminar on Modal Analysis, Leuven, Belgium, September, pp. 305-314.
18. Chen, T.-U., 1993, “Design SensitMty Analysis for Repeated Eigenvaues in Structural Design,” AIAA Journal, Vol. 31, No. 12, pp. 2347-2350.
19. Friswell, M. I., Garvey, S. D., and Penny, J. E. T., 1993, “Finite Element Model Updating of Rotor-Bearing Systems,” Conference on Modern Practice in Stress and Vibration Analysis, Sheffield, UK, April, pp. 557-568, Sheffield Academic Press.