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Nonlinear vibration modes and instability of a conceptual model of a spar platform

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Abstract

Spar floating platforms have been largely used for deepwater drilling, oil and natural gas production, and storage. In extreme weather conditions, such structures may exhibit a highly nonlinear dynamical behavior due to heave-pitch coupling. In this paper, a 2-DOF model is used to study the heave and pitch dynamical response in free and forced vibration. Special attention is given to the determination of the nonlinear vibration modes (NNMs). Nonsimilar and similar NNMs are obtained analytically by direct application of asymptotic and Galerkin-based methods. The results show important NNM features such as instability and multiplicity of modes. The NNMs are used to generate reduced order models consisting of SDOF nonlinear oscillators. This allows analytic parametric studies and the derivation of important features of the system such as its frequency-amplitude relations and resonance curves. The stability is analyzed by the Floquet theory. The analytical results show a good agreement with the numerical solution obtained by direct integration of the equation of motion. Instability analyses using bifurcation diagrams and Mathieu charts are carried out to understand the fundamental mechanism for the occurrence of unstable coupled heave-pitch resonant motions of floating structures in waves and to study the dependencies of the growth rate of unstable motions on physical parameters.

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Acknowledgements

The authors acknowledge the financial support of the Brazilian research agencies CAPES, CNPq, and FAPERJ and the help of Dr. Eulher C. Carvalho.

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Authors and Affiliations

  1. Pontifical Catholic University, Rio de Janeiro, RJ, Brazil

    Elvidio Gavassoni, Paulo B. Gonçalves & Deane M. Roehl

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  1. Elvidio Gavassoni
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  2. Paulo B. Gonçalves
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  3. Deane M. Roehl
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Correspondence to Paulo B. Gonçalves.

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Gavassoni, E., Gonçalves, P.B. & Roehl, D.M. Nonlinear vibration modes and instability of a conceptual model of a spar platform. Nonlinear Dyn 76, 809–826 (2014). https://doi.org/10.1007/s11071-013-1171-6

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