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Parametric Resonance in Dynamical Systems pp 267–285Cite as

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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    Rob H. B. Fey & Henk Nijmeijer

  2. Centre for Mechanical and Maritime Structures, TNO Built Environment and Geosciences, 49, 2600 AA, Delft, The Netherlands

    Niels J. Mallon

  3. IHC Lagersmit BV, 5, 2960 AA, Kinderdijk, The Netherlands

    C. Stefan Kraaij

Authors
  1. Rob H. B. Fey
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  2. Niels J. Mallon
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  3. C. Stefan Kraaij
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  4. Henk Nijmeijer
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Corresponding author

Correspondence to Rob H. B. Fey .

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Editors and Affiliations

  1. , Department of Engineering Cybernetics, Norwegian University of Science and Tech, Trondheim, 7491, Norway

    Thor I. Fossen

  2. Dynamics and Control Group, Techn. Univ. Eindhoven, Den Dolech 2, Eindhoven, 5600 MB, The Netherlands

    Henk Nijmeijer

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Fey, R.H.B., Mallon, N.J., Kraaij, C.S., Nijmeijer, H. (2012). Parametric and Direct Resonances in a Base-Excited Beam Carrying a Top Mass. In: Fossen, T., Nijmeijer, H. (eds) Parametric Resonance in Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1043-0_13

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  • DOI: https://doi.org/10.1007/978-1-4614-1043-0_13

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1042-3

  • Online ISBN: 978-1-4614-1043-0

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