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

  • C. J. J. Beckers
  • A. E. Öngüt
  • G. Verbeek
  • R. H. B. FeyEmail author
  • Y. Lemmens
  • N. van de Wouw
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 69)


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.


Bifurcation analysis Flexible multibody dynamics Shimmy Landing gear dynamics 



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


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • C. J. J. Beckers
    • 1
  • A. E. Öngüt
    • 4
  • G. Verbeek
    • 5
  • R. H. B. Fey
    • 1
    Email author
  • Y. Lemmens
    • 4
  • N. van de Wouw
    • 1
    • 2
    • 3
  1. 1.Dynamics and Control Group, Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Civil, Environmental and Geo-EngineeringUniversity of MinnesotaMinneapolisUSA
  3. 3.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands
  4. 4.Siemens PLM SoftwareLeuvenBelgium
  5. 5.Fokker Landing GearHelmondThe Netherlands

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