A detailed study of the parametric excitation of a vertical heavy rod using the method of multiple scales
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A detailed study of the parametric excitation of a vertical heavy rod using the method of multiple scales Guilherme Jorge Vernizzi
. Stefano Lenci . Guilherme Rosa Franzini
Received: 30 October 2019 / Accepted: 17 September 2020 Ó Springer Nature B.V. 2020
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 G. J. Vernizzi G. Rosa Franzini Offshore Mechanics Laboratory - LMO, Escola Polite´cnica, University of Sa˜o Paulo, Sa˜o Paulo, Brazil e-mail: [email protected] G. J. Vernizzi (&) S. Lenci Universita` Politecnica delle Marche, Ancona, Italy e-mail: [email protected] S. Lenci e-mail: [email protected]
small differences in the structural damping ratio can lead to significant differences in the response amplitude. Keywords Analytical solution Parametric excitation Multiple scales method Nonlinear hydrodynamic damping Vertical risers
1 Introduction Deep-water offshore engineering applications are a rich field of research in terms of structural dynamics. The use of very slender and flexible structures leads to scenarios with various types of dynamical responses. Some examples of typically studied scenarios are parametric excitation, loop formation, global buckling, local buckling of some internal layers of the structure and resonant phenomena such as vortexinduced vibrations (VIV). For these structures, the nonlinear behaviour due to their slenderness and the geometrical shape in the static equilibrium plays an important role in the response. The analysis of the possible responses can be made by means of different techniques. For instance, structures like risers, umbilical cables and tendons of tension leg platforms (TLP) have being studied by means of reduced-order models (ROMs), numerical simulations with the finite element method (FEM) and experimental investigations.
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Meccanica
We focus on the particular case of parametric excitation occurring due to the tim
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