DOI QR코드

DOI QR Code

Simultaneous identification of stiffness and damping based on derivatives of eigen-parameters

  • Lia, H. (Department of Applied Mechanics and Engineering, Sun Yat-sen University) ;
  • Liu, J.K. (Department of Applied Mechanics and Engineering, Sun Yat-sen University) ;
  • Lu, Z.R. (Department of Applied Mechanics and Engineering, Sun Yat-sen University)
  • Received : 2015.01.12
  • Accepted : 2015.05.15
  • Published : 2015.08.25

Abstract

A method based on derivatives of eigen-parameters is presented for damage detection in discrete systems with dampers. The damage is simulated by decrease on the stiffness coefficient and increase of the damping coefficient. In the forward analysis, the derivatives of eigen-parameters are derived for the discrete system. In the inverse analysis, a derivative of eigen-parameters based model updating approach is used to identify damages in frequency domain. Two numerical examples are investigated to illustrate efficiency and accuracy of the proposed method. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages and is insensitive to measurement noise. And satisfactory identified results can be obtained from few numbers of iterations.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Cawley, P. and Adams, R.D. (1979), "The location of defects in structures from measurements of natural frequencies", J. Strain Anal. Eng. Des., 14(2), 49-57. https://doi.org/10.1243/03093247V142049
  2. Di, W. and Law, S.S. (2007), "Eigen-parameter decomposition of element matrices for structural damage detection", Eng. Struct., 29(4), 519-528. https://doi.org/10.1016/j.engstruct.2006.05.019
  3. Dilena, M. and Morassi, A. (2006), "Damage detection in discrete vibrating systems", J. Sound Vib., 289(4), 830-850. https://doi.org/10.1016/j.jsv.2005.02.020
  4. Friswell, M. and Mottershead, J.E. (1995), Finite element model updating in structural dynamics, Springer Science and Business Media.
  5. Hansen, P.C. (1992), "Analysis of discrete ill-posed problems by means of the L-curve", SIAM Rev., 34(4), 561-580. https://doi.org/10.1137/1034115
  6. Hassiotis S. (1999), "Identification of damage using natural frequencies and system moments", Struct. Eng. Mech., 8(3), 285-297. https://doi.org/10.12989/sem.1999.8.3.285
  7. Lakshmanan, N., Raghuprasad, B.K., Gopalakrishnan, N., Sreekala, R. and Rao, G.V. (2010), "Comparative study on damage identification from lso-Eigen-Value-Change contours and smeared damage model", Struct. Eng. Mech., 35(6), 735-758. https://doi.org/10.12989/sem.2010.35.6.735
  8. Li, L., Zhu, H.P., Chen, H. and Miao, J.Y. (2007), "Sensitivity analysis of modal parameters for damage detection of shear-type frame structures", J. Huazhong Univers. Sci. Tech. (Urban Science Edition), 3, 011.
  9. Lifshitz, J.M. and Rotem, A. (1969), "Determination of reinforcement unbonding of composites by a vibration technique", J. Compos. Mater., 3(3), 412-423. https://doi.org/10.1177/002199836900300305
  10. Liu, J.K. and Yang, Q.W. (2006), "A new structural damage identification method", J. Sound Vib., 297(3), 694-703. https://doi.org/10.1016/j.jsv.2006.04.027
  11. Liu, X. (2013), "A new method for calculating derivatives of eigenvalues and eigenvectors for discrete structural systems", J. Sound Vib., 332(7), 1859-1867. https://doi.org/10.1016/j.jsv.2012.11.017
  12. Morassi, A. (2007), "Damage detection and generalized Fourier coefficients", J. Sound Vib., 302(1), 229-259. https://doi.org/10.1016/j.jsv.2006.11.015
  13. Nobahari, M. and Seyedpoor, S.M. (2013), "An efficient method for structural damage localization based on the concepts of flexibility matrix and strain energy of a structure", Struct. Eng. Mech., 46(2), 231-244. https://doi.org/10.12989/sem.2013.46.2.231
  14. Pandey, A.K., Biswas, M. and Samman, M.M. (1991), "Damage detection from changes in curvature mode shapes", J. Sound Vib., 145(2), 321-332. https://doi.org/10.1016/0022-460X(91)90595-B
  15. Raghuprasad, B.K., Lakshmanan, N., Gopalakrishnan, N. and Muthumani, K. (2008), "Sensitivity of eigen value to damage and its identification", Struct. Durab. Hlth. Moni., 4(3), 117-144.
  16. Salawu, O.S. (1997), "Detection of structural damage through changes in frequency: a review", Eng. Struct., 19(9), 718-723. https://doi.org/10.1016/S0141-0296(96)00149-6
  17. Tikhonov, A.N. (1963), "On the solution of ill-posed problems and the method of regularization", In Dokl. Akad. Nauk SSSR, 151, 501-504.
  18. Wong, C.N., Chen, J.C. and To, W.M. (1995), "Perturbation method for structural damage detection of multi-storey buildings", Proceedings of the International Conference on Structural Dynamics, Vibration, Noise and Control.
  19. Xia, Y. and Hao, H. (2003), "Statistical damage identification of structures with frequency changes", J. Sound Vib., 263(4), 853-870. https://doi.org/10.1016/S0022-460X(02)01077-5
  20. Yang, Q.W. (2009), "A mixed sensitivity method for structural damage detection", Commun. Num. Meth. Eng., 25(4), 381-389. https://doi.org/10.1002/cnm.1125
  21. Zhao, J. and DeWolf, J.T. (1999), "Sensitivity study for vibrational parameters used in damage detection", J. Struct. Eng., 125(4), 410-416. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(410)
  22. Zhu, H., Li, L. and He, X.Q. (2011), "Damage detection method for shear buildings using the changes in the first mode shape slopes", Comput. Struct., 89(9), 733-743. https://doi.org/10.1016/j.compstruc.2011.02.014

Cited by

  1. Identification of structural parameters including crack using one dimensional PZT patch model vol.25, pp.8, 2017, https://doi.org/10.1080/17415977.2016.1240794
  2. Structural damage identification using incomplete static displacement measurement vol.63, pp.2, 2015, https://doi.org/10.12989/sem.2017.63.2.251
  3. Cable Interlayer Slip Damage Identification Based on the Derivatives of Eigenparameters vol.18, pp.12, 2015, https://doi.org/10.3390/s18124456