Skip to main content

Bifurcation-Based Shimmy Analysis of Landing Gears Using Flexible Multibody Models

  • Chapter
  • First Online:
Nonlinear Structural Dynamics and Damping

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 69))

Abstract

Shimmy oscillations are undesired vibrations in aircraft landing gears. In this chapter, the onset of shimmy vibrations, marked by Hopf bifurcations, is investigated in the parameter space of high-fidelity, flexible multibody landing gear models. Such a bifurcation analysis is performed by combining the Virtual.Lab Motion multibody solver with the numerical continuation software AUTO. The resulting quasi-2-parameter bifurcation diagrams, involving aircraft velocity and normal load, are verified using conventional time-simulation methods and are shown to be computationally more efficient. A sensitivity study reveals the influence of design parameters, such as the shimmy damping coefficient, mechanical trail, and steering actuator stiffness, on the occurrence of shimmy.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Similar content being viewed by others

References

  1. Bampton, M.C.C., Craig Jr., R.R.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968). https://doi.org/10.2514/3.4741

    Article  MATH  Google Scholar 

  2. Beckers, C.J.J., Ongüt, A.E., Verbeek, B., Fey, R.H.B., Lemmens, Y., van de Wouw, N.: Bifurcation analysis of landing gear shimmy using flexible multibody models. In: Ambrósio, J. (ed.) 5th Joint International Conference on Multibody Systems and Dynamics (IMSD), 46. Portugal, June, 24–28 Lisboa (2018). http://imsd2018.tecnico.ulisboa.pt/Web_Abstracts_IMSD2018/pdf/WEB_PAPERS/IMSD2018_Full_Paper_46.pdf

  3. Coetzee, E., Thota, P., Rankin, J.: Dynamical Systems Toolbox. https://nl.mathworks.com/matlabcentral/fileexchange/32210-dynamical-systems-toolbox (2011). Accessed 14 June 2018

  4. Doedel, E., Keller, H.B., Kernevez, J.P.: Numerical analysis and control of bifurcation problems (I): bifurcation in finite dimensions. Int. J. Bifurc. Chaos 01(03), 493–520 (1991). https://doi.org/10.1142/S0218127491000397

    Article  MathSciNet  MATH  Google Scholar 

  5. Doedel, E.J., Oldeman, B.E.: AUTO-07P: Continuation and bifurcation software for ordinary differential equations. Technical Report, Concordia University, Montreal. http://indy.cs.concordia.ca/auto (2012). Accessed 14 June 2018

  6. Haug, E.J.: Computer Aided Kinematics and Dynamics of Mechanical Systems, 1st edn. Allyn and Bacon, 160 Gould Street, Needham Heights, Massachusetts 02194 (1989)

    Google Scholar 

  7. Howcroft, C., Lowenberg, M.H., Neild, S., Krauskopf, B., Coetzee, E.: Shimmy of an aircraft main landing gear with geometric coupling and mechanical freeplay. J. Comput. Nonlinear Dyn. 10(5), 051,011 (2015)

    Google Scholar 

  8. Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  9. Siemens Product Lifecycle Management Software Inc.: Case study—GKN Aerospace Fokker Landing Gear. https://www.plm.automation.siemens.com/pub/case-studies/64181?resourceId=64181 (2017). Accessed 6 Apr 2018

  10. Siemens Product Lifecycle Management Software Inc.: LMS Virtual.Lab Motion Online Help (documentation) (2017)

    Google Scholar 

  11. Tartaruga, I., Lowenberg, M.H., Cooper, J.E., Sartor, P., Lemmens, Y.: Bifurcation analysis of a nose landing gear system. In: 15th Dynamics Spectral Conference, American Institute of Aeronautics and Astronautics, San Diego, California, USA, AIAA SciTech Forum (2016). https://doi.org/10.2514/6.2016-1572

  12. Thomsen, J.J.: Vibrations and Stability, 2nd edn. Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-662-10793-5 (2003)

  13. Thota, P., Krauskopf, B., Lowenberg, M.H.: Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Nonlinear Dyn. 57(3), 455–467 (2009). https://doi.org/10.1007/s11071-008-9455-y

    Article  MATH  Google Scholar 

  14. Yoo, W.S., Haug, E.J.: Dynamics of articulated structures. Part I. Theory. J. Struct. Mech. 14(1), 105–126 (1986). https://doi.org/10.1080/03601218608907512

  15. Yoo, W.S., Haug, E.J.: Dynamics of flexible mechanical systems using vibration and static correction modes. J. Mech. Trans. Autom. 108(3), 315–322 (1986b). https://doi.org/10.1115/1.3258733

    Article  Google Scholar 

Download references

Acknowledgements

The work in this chapter was supported by Siemens PLM Software and Fokker Landing Gear. Their cooperation is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. H. B. Fey .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Beckers, C.J.J., Öngüt, A.E., Verbeek, G., Fey, R.H.B., Lemmens, Y., van de Wouw, N. (2019). Bifurcation-Based Shimmy Analysis of Landing Gears Using Flexible Multibody Models. In: Jauregui, J. (eds) Nonlinear Structural Dynamics and Damping. Mechanisms and Machine Science, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-030-13317-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-13317-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-13316-0

  • Online ISBN: 978-3-030-13317-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics