Parametric and Direct Resonances in a Base-Excited Beam Carrying a Top Mass

  • Rob H. B. FeyEmail author
  • Niels J. Mallon
  • C. Stefan Kraaij
  • Henk Nijmeijer


In this chapter, nonlinear resonances in a coupled shaker-beam-top mass system are investigated both numerically and experimentally. The imperfect, vertical beam carries the top mass and is axially excited by the shaker at its base. The weight of the top mass is below the beam’s static buckling load. A semi-analytical model is derived for the coupled system. In this model, Taylor-series approximations are used for the inextensibility constraint and the curvature of the beam. The steady-state behavior of the model is studied using numerical tools. In the model with a single beam mode, parametric and direct resonances are found, which affect the dynamic stability of the structure. The model with two beam modes not only shows an additional second harmonic resonance, but also reveals some extra small resonances in the low-frequency range, some of which can be identified as combination resonances. The experimental steady-state response is obtained by performing a (stepped) frequency sweep-up and sweep-down with respect to the harmonic input voltage of the amplifier-shaker combination. A good correspondence between the numerical and experimental steady-state responses is obtained.


Period Doubling Bifurcation Beam Mode Subharmonic Resonance Generalize DOFs Slender Beam 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research is supported by the Dutch Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs (STW project EWO.5792).


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Rob H. B. Fey
    • 1
    Email author
  • Niels J. Mallon
    • 2
  • C. Stefan Kraaij
    • 3
  • Henk Nijmeijer
    • 1
  1. 1.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Centre for Mechanical and Maritime StructuresTNO Built Environment and GeosciencesDelftThe Netherlands
  3. 3.IHC Lagersmit BVKinderdijkThe Netherlands

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