Nonlinear Model Updating Methodology with Application to the IMAC XXXIII Round Robin Benchmark Problem

  • Mehmet Kurt
  • Keegan J. Moore
  • Melih Eriten
  • D. Michael McFarland
  • Lawrence A Bergman
  • Alexander F Vakakis
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


We develop a new nonlinear model updating strategy based on global/local nonlinear system identification of general mechanical systems. The approach relies on analyzing system time series in the frequency-energy domain by constructing Hamiltonian, and forced/damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental results. By matching the frequency-energy plots of the benchmark system and its reduced order model, we show that we are able to retrieve the global dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series.


Nonlinear model updating Nonlinear system identification Frequency-energy plots Reduced-order modeling 


  1. 1.
    Mottershead JE, Friswell MI (1993) Model updating in structural dynamics: a survey. J Sound Vib 167(2):347–375CrossRefGoogle Scholar
  2. 2.
    Friswell M, Mottershead JE (1995) Finite element model updating in structural dynamics. Springer, DordrechtMATHCrossRefGoogle Scholar
  3. 3.
    Hemez FM, Doebling SW (2001) Review and assessment of model updating for non-linear, transient dynamics. Mech Syst Signal Process 15(1):45–74CrossRefGoogle Scholar
  4. 4.
    Datta BN (2002) Finite-element model updating, eigenstructure assignment and eigenvalue embedding techniques for vibrating systems. Mech Syst Signal Process 16(1):83–96CrossRefGoogle Scholar
  5. 5.
    Teughels A, Maeck J, De Roeck G (2002) Damage assessment by FE model updating using damage functions. Comput Struct 80(25):1869–1879CrossRefGoogle Scholar
  6. 6.
    Brownjohn JMW, Xia P-Q, Hao H, Xia Y (2001) Civil structure condition assessment by FE model updating: methodology and case studies. Finite Elem Anal Des 37(10):761–775MATHCrossRefGoogle Scholar
  7. 7.
    Link M, Rohrmann RG, Pietrzko S (1996) Experience with automated procedures for adjusting the finite element model of a complex highway bridge to experimental modal data. In: Proceedings-Spie of the international society for optical engineering, Spie International Society For Optical, pp 218–225Google Scholar
  8. 8.
    Kerschen G, McFarland DM, Kowtko JJ, Lee YS, Bergman LA, Vakakis AF (2007) Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity. J Sound Vib 299(4–5):822–838CrossRefGoogle Scholar
  9. 9.
    Andersen D, Starosvetsky Y, Vakakis A, Bergman L (2012) Dynamic instabilities in coupled oscillators induced by geometrically nonlinear damping. Nonlin Dyn 67(1):807–827MathSciNetCrossRefGoogle Scholar
  10. 10.
    Remick K, Vakakis A, Bergman L, McFarland DM, Quinn DD, Sapsis TP (2013) Sustained high-frequency dynamic instability of a nonlinear system of coupled oscillators forced by single or repeated impulses: theoretical and experimental results. J Vib Acoust 136(1):011013–011013CrossRefGoogle Scholar
  11. 11.
    Peeters M, Viguié R, Sérandour G, Kerschen G, Golinval J-C (2009) Nonlinear normal modes, Part II: toward a practical computation using numerical continuation techniques. Mech Syst Signal Process 23(1):195–216CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Mehmet Kurt
    • 1
  • Keegan J. Moore
    • 2
  • Melih Eriten
    • 3
  • D. Michael McFarland
    • 4
  • Lawrence A Bergman
    • 4
  • Alexander F Vakakis
    • 2
  1. 1.Department of BioengineeringStanford UniversityStanfordUSA
  2. 2.Department of Mechanical Science and EngineeringUniversity of IllinoisUrbanaUSA
  3. 3.Department of Mechanical EngineeringUniversity of Wisconsin at MadisonMadisonUSA
  4. 4.Department of Aerospace EngineeringUniversity of IllinoisUrbanaUSA

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