This paper discusses a theoretical approach to investigate the dependency relationship between the stiffness matrix and the complex eigenvectors in the identification of structural systems for the case of insufficient instrumentation setup. The main result of the study consists of proving, in the case of classical damping, the independency of the stiffness subpartition corresponding to the measured degrees-of-freedom from the unmeasured ones. The same result is shown to be valid in the case of nonclassical damping but only for tridiagonal sparse stiffness matrix systems. A numerical procedure proves the above results and also shows the dependency relationship for the general nonclassical damping cases.
1.
Alvin
, K. F.
, and Park
, K. C.
, 1994, “Second-Order Structural Identification Procedure via State-Space-Based System Identification
,” AIAA J.
0001-1452, 32
(2
), pp. 397
–406
.2.
Alvin
, K. F.
, Peterson
, L. D.
, and Park
, K. C.
, 1995, “Method for Determining Minimum-Order Mass and Stiffness Matrices From Modal Test Data
,” AIAA J.
0001-1452, 33
(1
), pp. 128
–135
.3.
Farhat
, C.
, and Hemez
, F. M.
, 1993, “Updating Finite Element Dynamic Models Using an Element-by-Element Sensitivity Methodology
,” AIAA J.
0001-1452, 31
(9
), pp. 1702
–1711
.4.
Red-Horse
, J. R.
, and Alvin
, K. C.
, 1996, “Finite Element Modeling, Reconciliation and Evaluation of Predictive Accuracy: A Case Study
,” Proceedings of the AIAA/ASEM 1996 Adaptive Structure Forum
, AIAA, pp. 263
–269
.5.
Doebling
, S. W.
, Hemez
, F. M.
, Barlow
, M. S.
, Petersonorse
, L. D.
, and Farhat
, C.
, 1993, “Damage Detection in a Suspended Scale Model Truss via Modal Update
,” Proceedings of the 11th International Modal Analysis Conference
,” Society for Experimental Mechanics, pp. 1083
–1094
.6.
Kaouk
, M.
, and Zimmerman
, D. C.
, 1994, “Structural Damage Assessment Using a Generalized Minimum Rank Perturbation Theory
,” AIAA J.
0001-1452, 32
(4
), pp. 836
–842
.7.
Agbabian
, M. S.
, Masri
, S. F.
, Miller
, R. K.
, and Caughey
, T. K.
, 1991, “System Identification Approach to Detection of Structural Changes
,” J. Eng. Mech.
0733-9399, 117
(2
), pp. 370
–390
.8.
DeAngelis
, M.
, Luş
, H.
, Betti
, R.
, and Longman
, R. W.
, 2002, “Extracting Physical Parameters of Mechanical Models From Identified State Space Representations
,” ASME J. Appl. Mech.
0021-8936, 69
(5
), pp. 617
–625
.9.
Tseng
, D. H.
, Longman
, R. W.
, and Juang
, J. N.
, 1994, “Identification of Gyroscopic and Nongyroscopic Second Order Mechanical Systems Including Repeated Problems
,” Adv. Astronaut. Sci.
0065-3438, 87
, pp. 145
–165
.10.
Guyan
, R. J.
, 1965, “Reduction of Stiffness and Mass Matrices
,” AIAA J.
0001-1452, 3
(2
), p. 380
.11.
12.
Balmés
, E.
, 1997, “New Result on the Identification of Normal Modes From Experimental Complex Modes
,” Mech. Syst. Signal Process.
0888-3270, 11
(2
), pp. 229
–243
.13.
Sestieri
, A.
, and Ibrahim
, S. R.
, 1994, “Analysis of Errors and Approximations in the Use of Modal Co-Ordinates
,” J. Sound Vib.
0022-460X, 177
(2
), pp. 145
–157
.14.
Alvin
, K. F.
, and Park
, K. C.
, 1999, “Extraction of Substructural Flexibility From Global Frequencies and Mode Shapes
,” AIAA J.
0001-1452, 37
(11
), pp. 1444
–1451
.15.
Bernal
, D.
, 2001, “Damage Localization in Out-Put Only Systems
,” Proceedings of the Third International Workshop in Structural Health Monitoring
, Stanford, CA.16.
Luş
, H.
, 2001, “Control Theory Based System Identification
,” Ph.D. thesis, Columbia University, New York.17.
Luş
, H.
, De Angelis
, M.
, and Betti
, R.
, 2003, “A New Approach for Reduced Order Modelling of Mechanical System Using Vibration Measurements
,” ASME J. Appl. Mech.
0021-8936, 70
(5
), pp. 715
–723
.18.
Yu
, J.
, 2004, “Identification of Reduced Order Model of Linear Structural Systems
,” Ph.D. thesis, Columbia University, New York.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
