FE model updating method incorporating damping matrices for structural dynamic modifications

  • Arora, Vikas (Department of Technology and Innovation, University of Southern Denmark)
  • Received : 2013.02.12
  • Accepted : 2014.05.09
  • Published : 2014.10.25


An accurate finite element (FE) model of a structure is essential for predicting reliably its dynamic characteristics. Such a model is used to predict the effects of structural modifications for dynamic design of the structure. These modifications may be imposed by design alterations for operating reasons. Most of the model updating techniques neglect damping and so these updated models can't be used for accurate prediction of vibration amplitudes. This paper deals with the basic formulation of damped finite element model updating method and its use for structural dynamic modifications. In this damped damped finite element model updating method, damping matrices are updated along with mass and stiffness matrices. The damping matrices are updated by updating the damping coefficients. A case involving actual measured data for the case of F-shaped test structure, which resembles the skeleton of a drilling machine is used to evaluate the effectiveness of damped FE model updating method for accurate prediction of the vibration levels and thus its use for structural dynamic modifications. It can be concluded from the study that damped updated FE model updating can be used for structural dynamic modifications with confidence.


  1. Adhikari, S. and Friswell, M.I. (2010), "Distributed parameter model updating using the Karhunen-Loeve expansion", Mech. Sys. Sig. Pro., 24, 326-339.
  2. Arora, V., Singh, S.P. and Kundra, T.K. (2009a), "Damped model updating using complex updating parameters", J. Sound Vib., 320, 438-451.
  3. Arora, V., Singh, S.P. and Kundra, T.K. (2009b), "Damped FE model updating using complex updating parameters: its use for dynamic design", J. Sound Vib., 324, 350-364.
  4. Arora, V., Singh, S.P. and Kundra, T.K. (2010), "Further experience with model updating incorporating damping matrices", Mech. Sys. Sig. Pro., 24, 1383-1390.
  5. Baruch, M. (1978), "Optimization procedure to correct stiffness and flexibility matrices using vibration data", AIAA J., 16, 1208-1210.
  6. Berman, A. and Nagy, E.J. (1983), "Improvement of a large analytical model using test data", AIAA J., 21, 927-928.
  7. Bert, C.W. (1973), "Material damping: An introduction review of mathematical models, measures and experimental techniques", J. Sound Vib., 29, 129-153.
  8. Collins, J.D., Hart, G.C., Hasselman, T.K. and Kennedy B. (1974), "Statistical identification of structures", AIAA J., 12, 185-190.
  9. Govers, Y. and Link, M. (2010) "Stochastic model updating-Covariance matrix adjustment from uncertain experimental modal data", Mech. Sys. Sig. Pro., 3, 696-706.
  10. Lin, R.M. and Ewins, D.J. (1994), "Analytical model improvement using frequency response functions", Mech. Sys. Sig. Pro., 8, 437-458.
  11. Lepoittevin, G. and Kess, G. (2011), "Finite element model updating of vibrating structures under free-free boundary conditions for modal damping prediction", Mech. Sys. Sig. Pro., 25, 2203-2218.
  12. Matta, E. and Stefno, A.D. (2012), "Robust finite element model updating of a large-scale benchmark building structure", Struct. Eng. Mech., 43(3), 371-394.
  13. Modak, S.V., Kundra, T.K. and Nakra, B.C. (2005), "Studies in dynamic design using updated models", J. Sound Vib., 281, 943-964.
  14. Pradhan, S. and Modak, S.V. (2012), "A method of damping matrix identification using frequency response data", Mech. Sys. Sig. Pro., 33, 69-82.
  15. Titurus, B. and Friswell, M.I. (2008), "Regularisation in model updating", Int. J. Numer. Meth. Eng., 75, 440-478.
  16. Yong, L. and Zhenguo T. (2004), "A two-level neural network approach to dynamic FE model updating including damping", J. Sound Vib., 275, 931-952.
  17. Wang, J. and Yang, Q.S., (2012), "Modified Tikhonov regularization in model updating for damage identification", Struct. Eng. Mech., 44(5), 585-600.
  18. Zang, B.Q., Chan, G.P. and Guo, Q.T. (2012), "Finite element model updating for unsymmetrical damping system with genetic algorithm", A. Mech. Mat., 166-169, 2999-3003.