Influences of Modal Coupling on Experimentally Extracted Nonlinear Modal Models

  • Benjamin J. MoldenhauerEmail author
  • Aabhas Singh
  • Phil Thoenen
  • Daniel R. Roettgen
  • Benjamin R. Pacini
  • Robert J. Kuether
  • Matthew S. Allen
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Research has shown that mechanical structures can be modeled as a combination of weakly nonlinear uncoupled modal models. These modal models can take many forms such as a basic cubic stiffness and damping force model, or a modal Iwan model. This method relies on two assumptions: (1) the mode shapes of the structure are not amplitude dependent, and (2) the modes of the structure do not couple or interact in the amplitude range of interest. Recently, a hypothesis was proposed that when multiple modes are excited that exercise the same nonlinear joint, the modes begin to couple. This hypothesis is tested on a physical system using a series of narrow-band excitation techniques via a modal shaker and broad-band excitation from a modal hammer. The resulting amplitude dependent stiffness and damping from the various excitation types are used to characterize the degree of modal coupling. Significant modal coupling is observed between three of the low order modes of a cylindrical structure with a beam connected to a plate on its end, which exhibits nonlinearity due to micro-slip in bolted joints.


Modal coupling Nonlinear modal model Iwan model Nonlinear simulation Hilbert analysis Nonlinear reduced order models 



This research was conducted at the 2018 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute supported by Sandia National Laboratories. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The authors would also like to thank Bill Flynn from Siemens Industry Software NV for supplying the data acquisition and testing systems used to collect the experimental measurements presented throughout this work.


  1. 1.
    Eriten, M., Kurt, M., Luo, G., Michael McFarland, D., Bergman, L.A., Vakakis, A.F.: Nonlinear system identification of frictional effects in a beam with a bolted joint connection. Mech. Syst. Signal Process. 39(1–2), 245–264 (2013)CrossRefGoogle Scholar
  2. 2.
    Lacayo, R., Deaner, B., Allen, M.S.: A numerical study on the limitations of modal Iwan models for impulsive excitations. J. Sound Vib. 390, 118–140 (2017)CrossRefGoogle Scholar
  3. 3.
    Feldman, M.: Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method ‘Freevib’. Mech. Syst. Signal Process. 8(2), 119–127 (1994)CrossRefGoogle Scholar
  4. 4.
    Pacini, B.R., Mayes, R.L., Owens, B.C., R. Schultz: Nonlinear Finite Element Model Updating, Part I: Experimental Techniques and Nonlinear Modal Model Parameter Extraction. In: Presented at the International Modal Analysis Conference XXXV, Garden Grove, CA, 2017Google Scholar
  5. 5.
    Phillips, A.W., Allemang, R.J.: Single Degree-of-Freedom Modal Parameter Estimation Methods. In: Presented at the 14th International Modal Analysis Conference (IMAC-14), 1996, pp. 253–260Google Scholar
  6. 6.
    Ginsberg, J.H.: Engineering Dynamics, 3rd edn. Cambridge University Press, Cambridge, MA (2005)zbMATHGoogle Scholar
  7. 7.
    Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.-C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20, 505–592 (2006)CrossRefGoogle Scholar
  8. 8.
    Singh, A. et al.: Experimental Characterization of a new Benchmark Structure for Prediction of Damping Nonlinearity. In: Presented at the 36th International Modal Analysis Conference (IMAC XXXVI), Orlando, Florida (2018)Google Scholar
  9. 9.
    Yang, J.N., Lei, Y., Pan, S., Huang, N.: System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: Normal modes. Earthq. Eng. Struct. Dyn. 32(9), 1443–1467 (2003)CrossRefGoogle Scholar
  10. 10.
    Feldman, M.: Time-varying vibration decomposition and analysis based on the Hilbert transform. J. Sound Vib. 295(3–5), 518–530 (2006)CrossRefGoogle Scholar
  11. 11.
    Allen, M.S.: Global and Multi-Input-Multi-Output (MIMO) Extensions of the Algorithm of Mode Isolation (AMI). Georgia Institute of Technology, Atlanta (2005)Google Scholar
  12. 12.
    Fischer, E.G.: Sine beat vibration testing related to earthquake resonance spectra. Shock Vib. Bull. 42(2), 1–8 (1972)Google Scholar
  13. 13.
    Harris, F.: On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE. 66(1), 51–83 (1978)CrossRefGoogle Scholar
  14. 14.
    Worden, K., Wright, J.R., Al-Hadid, M.A., Mohammad, K.S.: Experimental identification of multi degree-of-freedom nonlinear systems using restoring force methods. Int. J. Anal. Exp. Modal Anal. 9(1), 35–55 (1994)Google Scholar
  15. 15.
    Allen, M., Sumali, H., Epp, D.S.: Restoring Force Surface Analysis of Nonlinear Vibration Data from Micro-Cantilever Beams. In: Presented at the 2006 ASME International Mechanical Engineering Congress and Exposition, 2006Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  • Benjamin J. Moldenhauer
    • 1
    Email author
  • Aabhas Singh
    • 1
  • Phil Thoenen
    • 2
  • Daniel R. Roettgen
    • 3
  • Benjamin R. Pacini
    • 3
  • Robert J. Kuether
    • 3
  • Matthew S. Allen
    • 1
  1. 1.Department of Engineering PhysicsUniversity of WisconsinMadisonUSA
  2. 2.Department of Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Sandia National LaboratoriesAlbuquerqueUSA

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