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A detailed study of the parametric excitation of a vertical heavy rod using the method of multiple scales

  • Recent Advances in Nonlinear Dynamics and Vibrations
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Abstract

An analytical solution for the problem of an immersed flexible and vertical heavy rod subjected to a vertical top motion is developed using the multiple scales method directly applied to the partial differential equations of motion. The obtained results show good agreement with a numerical solution obtained using the finite element method for a study case. The analytical solution is then used to carry out some sensitivity studies. The effects of the structural nonlinearities, hydrodynamic and structural damping terms are investigated. It is shown that the nonlinearities play a role in defining the frequency of the top motion that causes the maximum amplitude of response, but not the value of the amplitude itself. In turn, the major role played by the hydrodynamic damping in defining the response amplitude is addressed. It is also shown that the structural damping have an important effect on the response amplitude even in the case of small damping ratio. This occurs due to the combined effect of the structural with the hydrodynamic damping. Finally, it is pointed out that small differences in the structural damping ratio can lead to significant differences in the response amplitude.

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Acknowledgements

The first author acknowledges the São Paulo Research Foundation (FAPESP) for research grants n. 2016/25457-1 and 2017/16578-2, the latter a financial support to his internship at Università Politecnica delle Marche.

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Authors and Affiliations

  1. Offshore Mechanics Laboratory - LMO, Escola Politécnica, University of São Paulo, São Paulo, Brazil

    Guilherme Jorge Vernizzi & Guilherme Rosa Franzini

  2. Università Politecnica delle Marche, Ancona, Italy

    Guilherme Jorge Vernizzi & Stefano Lenci

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  1. Guilherme Jorge Vernizzi
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  2. Stefano Lenci
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  3. Guilherme Rosa Franzini
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Correspondence to Guilherme Jorge Vernizzi.

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Vernizzi, G.J., Lenci, S. & Rosa Franzini, G. A detailed study of the parametric excitation of a vertical heavy rod using the method of multiple scales. Meccanica 55, 2423–2437 (2020). https://doi.org/10.1007/s11012-020-01247-6

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