Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped and damped structures assuming damage results in a localized change in a subset (not full set) of the property matrices (mass, stiffness and damping matrices). The algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite element model. In this work, the concept of the Minimum Rank Perturbation Theory (MRPT) is adopted to simultaneously determine the damage extent of all property matrices of undamped and proportionally damped structures. Note that the property matrices are the mass, stiffness and damping matrices. Illustrative examples are presented to show the performance of the proposed theory. [S0739-3717(00)01904-8]

1.
Ibrahim, S. R., and Saafan, A. A., 1987, “Correlation of Analysis and Test in Modeling of Structures, Assessment and Review,” Proceedings of the 5th IMAC, pp. 1651–1660.
2.
Heylen, W., and Sas, P., 1987, “Review of Model Optimization Techniques,” Proceedings of the 5th IMAC, pp. 1177–1182.
3.
Baruch
,
M.
, and
Bar Itzhack
,
I. Y.
,
1978
, “
Optimum Weighted Orthogonalization of Measured Modes
,”
AIAA J.
,
16
, No.
4
, pp.
346
351
.
4.
Martinez, D., Red-Horse, J., and Allen, J., 1991, “System Identification Methods for Dynamic Structural Models of Electronic Packages,” Proceedings of the 32nd AIAA Structures, Structural Dynamics and Materials Conference, Baltimore, MD, pp. 2336–2346.
5.
Matzen, V. C., 1987, “Time Domain Identification of Reduced Parameter Models,” Proceedings of the SEM Spring Conference on Experimental Mechanics, Houston, Texas, pp. 401–408.
6.
Zimmerman
,
D. C.
, and
Widengren
,
W.
,
1990
, “
Model Correction Using a Symmetric Eigenstructure Assignment Technique
,”
AIAA J.
,
28
, No.
9
, pp.
1670
1676
.
7.
Inman, D. J., and Minas, C., 1990, “Matching Analytical Models with Experimental Modal Data in Mechanical Systems,” Control and Dynamic Systems: Advances in Industrial Systems, Vol. 37, C. T. Leondes, Ed., Academic Press, pp. 327–363.
8.
Zimmerman
,
D. C.
, and
Kaouk
,
M.
,
1994
, “
Structural Damage Detection Using a Minimum Rank Update Theory
,”
ASME J. Vibr. Acoust.
,
116
, No.
2
, pp.
222
231
.
9.
Kaouk, M., and Zimmerman, D. C., “Structural Damage Assessment Using a Generalized Minimum Rank Perturbation Theory,” Proceedings of the 34th AIAA Structures, Structural Dynamics and Materials Conference, La Jolla, CA, pp. 1529–1539, April, 1993.
10.
Smith, S. W., and Beattie, C. A., 1990, “Simultaneous Expansion and Orthogonalization of Measured Modes for Structural Identification,” Proceedings of the AIAA Dynamic Specialist Conference, Long Beach, CA, pp. 261–270.
11.
Berman
,
A.
, and
Nagy
,
E. J.
,
1983
, “
Improvements of a Large Analytical Model Using Test Data
,”
AIAA J.
,
21
, No.
8
, pp.
1168
1173
.
12.
McGowan, P. E., “Dynamic Test/Analysis Correlation using Reduced Analytical Models,” M.S. Thesis, Engineering Mechanics, Old Dominion University.
13.
O’Callahan, J. C., 1989, “A Procedure for an Improved Reduced System (IRS) Model,” Proceedings of the Seventh International Modal Analysis Conference, Las Vegas, NA, pp. 17–21.
14.
Ojalvo, I. U., and Pilon, D., 1988, “Diagnostics for Geometrically Locating Structural Math Model Errors From Modal Test Data,” Proceedings of the 29th AIAA Structures, Structural Dynamics and Materials Conference, Williamsburg, VA, pp. 1174–1186.
15.
Kaouk, M., Finite Element Model Adjustment and Damage Detection Using Measured Test Data, Ph.D. Dissertation, AeMES, University of Florida, 1993.
16.
Golub, G. H., and Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1989.
17.
Ricles, J. M., 1991, “Nondestructive Structural Damage Detection In Flexible Space Structures Using Vibration Characterization,” Report NGT-44-001-800 submitted to NASA/JSC.
You do not currently have access to this content.