Skip to main content

Nonlinear Substructuring Using Fixed Interface Nonlinear Normal Modes

  • Conference paper
  • First Online:
Dynamics of Coupled Structures, Volume 4

Abstract

This study introduces a nonlinear dynamic substructuring (NDS) method assembling a truncated number of nonlinear normal modes (NNMs). A generic nonlinear structure is first divided into substructures and each substructure is reduced by taking a truncated number of fixed interface NNMs in addition to the proposed nonlinear constraint modes at each energy level. Using this basis a reduced quasi linear model of the substructures is computed at each energy level. Then the assembly of the quasi linear substructures using the Component Mode Synthesis (CMS) method yields the NNMs of the whole structure. The proposed method can be considered as an extension of the Craig-Bampton (CB) method for nonlinear structures. In order to evaluate the performance of the proposed nonlinear Craig-Bampton (NCB) approach, it is applied on a numerical example and the substructuring results are validated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Prezmienecki, J.S.: Matrix structural analysis of substructures. AIAA J. 1 (1), 138–147 (1963)

    Article  Google Scholar 

  2. MacNeal, R.H.: A hybrid method of component mode synthesis. In: Computers & Structures, vol. I, pp. 581–601. Pergamon Press, New York (1971)

    Google Scholar 

  3. Rubin, S.: Improved component-mode representation for structural dynamic analysis. AIAA J. 13 (8), 995–1006 (1975)

    Article  MATH  Google Scholar 

  4. Chang, C., Craig, R.R.: On the use of attachement modes in substructure coupling for dynamics analysis. In: 18th Structures, Structural Dynamics and Material Conference, San Diego, 21–23 Mar, pp. 89–99. AIAA/ASME

    Google Scholar 

  5. Rixen, D.J.: A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168, 383–391 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bampton, M.C.C., Craig, R.R., Jr.: Coupling of substructures for dynamic analyses. AIAA J. 6 (7), 1313–1319 (1968)

    Article  MATH  Google Scholar 

  7. Ewins, D.J., Ferreira, J.V.: Nonlinear receptance coupling approach based on describing functions. In: Proceedings of SPIE – the International Society for Optical Engineering, pp. 1034–1040 (1996)

    Google Scholar 

  8. Allen, M.S., Keuther, R.J.: Craig-Bampton substructuring for geometrically nonlinear subcomponents. In: 32nd IMAC, A Conference and Exposition on Structural Dynamics, Orlando. Conference Proceedings of the Society for Experimental Mechanics, pp. 167–178 (2014)

    Google Scholar 

  9. Rosenberg, R.M.: Normal modes of nonlinear dual-mode systems. J. Appl. Mech. 27, 263–268 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rosenberg, R.M.: The normal modes of nonlinear n-degree.of-freedom systems. J. Appl. Mech. 30 (1), 7–14 (1962)

    Google Scholar 

  11. Shaw, S., Pierre, C.: Non-linear normal modes and invariant manifold. J. Sound Vib. 150 (1), 170–173 (1991)

    Article  Google Scholar 

  12. Allen, M.S., Keuther, R.J.: Nonlinear modal substructuring of systems with geometric nonlinearities. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Boston, 8–11 Apr 2013

    Google Scholar 

  13. Apiwattanalunggarn, P.: Model reduction of nonlinear structural system using nonlinear normal modes and component mode synthesis. Ph.D. thesis, Michigan State University (2003)

    Google Scholar 

  14. Kerschen, G., Golinval, J.-C., Peeters, M., Vigu, R., Serandour, G.: Nonlinear normal modes, Part II: towards a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23 (1), 195–216 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Falco .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Falco, M., Karamooz Mahdiabadi, M., Rixen, D.J. (2017). Nonlinear Substructuring Using Fixed Interface Nonlinear Normal Modes. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54930-9_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-54930-9_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54929-3

  • Online ISBN: 978-3-319-54930-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics