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.
[1] M. I. Friswell, J. E. Mottershead. Finite Element Moodel Updating in
Structural Dynamics, Dordrecht: Klumer Academic Publishers, 1995.
[2] M. Baruch. Optimal correction of mass and stiffness matrices using
measured modes, AIAA Journal. 16 (1982) 1623-1626.
[3] M. Baruch, I. Y. Bar-Itzhack. Optimal weighted orthogonalization of
measured modes, AIAA Journal. 16 (1978) 346-351.
[4] A. Berman. Mass matrix correction using an incomplete set of measured
modes, AIAA Journal. 17 (1979) 1147-1148.
[5] A. Berman, E. J. Nagy. Improvement of a large analytical model using
test data, AIAA Journal. 21 (1983) 1168-1173.
[6] B. Caeser, J. Pete. Direct update of dynamic mathematical models from
modal test data, AIAA Journal. 25 (1987) 1494-1499.
[7] F. S. Wei. Stiffness matrix correction from incomplete test data, AIAA
Journal. 18 (1980) 1274-1275.
[8] F. S. Wei. Analytical dynamic model improvement using vibration test
data. AIAA Journal. 28 (1990) 174-176.
[9] F. S. Wei. Mass and stiffness interaction effects in analytical model
modification. AIAA Journal. 28 (1990) 1686-1688.
[10] 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.
[11] Y. Yuan. A model updating method for undamped structural systems,
Journal of Computational and Applied Mathematics. 219 (2008) 294-
301.
[12] 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.
[13] 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.
[14] 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.
[15] A. Ben-Israel, T. N. E. Greville. Generalized Inverses. Theory and
Applications (second ed), New York: Springer, 2003.
[16] P. Lancaster, M. Tismenetsky. The theory of matrices, 2nd ed., Academic
Press, New York, 1985.
[17] J. P. Aubin. Applied Functional Analysis, John Wiley & Sons, Inc, 1979.
[1] M. I. Friswell, J. E. Mottershead. Finite Element Moodel Updating in
Structural Dynamics, Dordrecht: Klumer Academic Publishers, 1995.
[2] M. Baruch. Optimal correction of mass and stiffness matrices using
measured modes, AIAA Journal. 16 (1982) 1623-1626.
[3] M. Baruch, I. Y. Bar-Itzhack. Optimal weighted orthogonalization of
measured modes, AIAA Journal. 16 (1978) 346-351.
[4] A. Berman. Mass matrix correction using an incomplete set of measured
modes, AIAA Journal. 17 (1979) 1147-1148.
[5] A. Berman, E. J. Nagy. Improvement of a large analytical model using
test data, AIAA Journal. 21 (1983) 1168-1173.
[6] B. Caeser, J. Pete. Direct update of dynamic mathematical models from
modal test data, AIAA Journal. 25 (1987) 1494-1499.
[7] F. S. Wei. Stiffness matrix correction from incomplete test data, AIAA
Journal. 18 (1980) 1274-1275.
[8] F. S. Wei. Analytical dynamic model improvement using vibration test
data. AIAA Journal. 28 (1990) 174-176.
[9] F. S. Wei. Mass and stiffness interaction effects in analytical model
modification. AIAA Journal. 28 (1990) 1686-1688.
[10] 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.
[11] Y. Yuan. A model updating method for undamped structural systems,
Journal of Computational and Applied Mathematics. 219 (2008) 294-
301.
[12] 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.
[13] 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.
[14] 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.
[15] A. Ben-Israel, T. N. E. Greville. Generalized Inverses. Theory and
Applications (second ed), New York: Springer, 2003.
[16] P. Lancaster, M. Tismenetsky. The theory of matrices, 2nd ed., Academic
Press, New York, 1985.
[17] J. P. Aubin. Applied Functional Analysis, John Wiley & Sons, Inc, 1979.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60857", author = "Yongxin Yuan and Jiashang Jiang", title = "A New Direct Updating Method for Undamped Structural Systems", abstract = "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.
", keywords = "Finite element model, model updating, modal data, optimal approximation.", volume = "4", number = "1", pages = "113-6", }
