A New Direct Updating Method for Undamped Structural Systems
A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078001Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1190
 M. I. Friswell, J. E. Mottershead. Finite Element Moodel Updating in Structural Dynamics, Dordrecht: Klumer Academic Publishers, 1995.
 M. Baruch. Optimal correction of mass and stiffness matrices using measured modes, AIAA Journal. 16 (1982) 1623-1626.
 M. Baruch, I. Y. Bar-Itzhack. Optimal weighted orthogonalization of measured modes, AIAA Journal. 16 (1978) 346-351.
 A. Berman. Mass matrix correction using an incomplete set of measured modes, AIAA Journal. 17 (1979) 1147-1148.
 A. Berman, E. J. Nagy. Improvement of a large analytical model using test data, AIAA Journal. 21 (1983) 1168-1173.
 B. Caeser, J. Pete. Direct update of dynamic mathematical models from modal test data, AIAA Journal. 25 (1987) 1494-1499.
 F. S. Wei. Stiffness matrix correction from incomplete test data, AIAA Journal. 18 (1980) 1274-1275.
 F. S. Wei. Analytical dynamic model improvement using vibration test data. AIAA Journal. 28 (1990) 174-176.
 F. S. Wei. Mass and stiffness interaction effects in analytical model modification. AIAA Journal. 28 (1990) 1686-1688.
 J. Carvalho, B. N. Datta, A. Gupta, M. Lagadapati. A direct method for model updating with incomplete measured data and without spurious modes, Mechanical Systems and Signal Processing. 21 (2007) 2715- 2731.
 Y. Yuan. A model updating method for undamped structural systems, Journal of Computational and Applied Mathematics. 219 (2008) 294- 301.
 Y.B. Yang, Y. J. Chen. A new direct method for updating structural models based on measured modal data, Engineering Structures. 31 (2009) 32-42.
 J. Moreno, B. N. Datta, M. Raydan. A symmetry preserving alternating projection method for matrix model updating, Mechanical Systems and Signal Processing. 23 (2009) 1784-1791.
 Y.B. Yang, Y. J. Chen, T. W. Hsu. Direct updating method for structural models based on orthogonality constraints, Mechanics of Advanced Materials and Structures, 16 (2009) 390-401.
 A. Ben-Israel, T. N. E. Greville. Generalized Inverses. Theory and Applications (second ed), New York: Springer, 2003.
 P. Lancaster, M. Tismenetsky. The theory of matrices, 2nd ed., Academic Press, New York, 1985.
 J. P. Aubin. Applied Functional Analysis, John Wiley & Sons, Inc, 1979.