Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction

Bulian, Gabriele

doi:10.1016/j.nonrwa.2004.03.002

Cited by 23 publications

(13 citation statements)

References 8 publications

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“…On these assumptions, only roll motion is taken into account in the present analysis. The influence of roll on pitch and heave could be modeled as an explicit forcing, whereas the influence of heave and pitch on roll can be modeled as a parametric excitation by utilizing quasi-static Froude-Krylov assumption [20,21]. The essence of quasi-static assumption is balancing heave and pitch statically in a wave.…”

Section: Description Of Modelsmentioning

confidence: 99%

“…An alternative simplified approach is possible for reducing number of DOF from 3 to 1 with the quasi-static FroudeKrylov assumption [20,21]. Based on these assumptions, both direct and indirect effects of waves may be evaluated.…”

Section: Introductionmentioning

confidence: 99%

“…6 DOF and 4 DOF time domain simulation approaches were applied by using AQWA-LINE and AQWA-NAUT software which are capable of calculating motions by using 3D diffraction/radiation and potential flow theory. The single -DOF time and frequency domain models based on reducing number of DOF from 3 to 1 by using the quasi-static Froude-Krylov assumption [20,21,22] were used for analytical approaches. In the models, heave and pitch effects were considered by means of time varying restoring moment [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…The single -DOF time and frequency domain models based on reducing number of DOF from 3 to 1 by using the quasi-static Froude-Krylov assumption [20,21,22] were used for analytical approaches. In the models, heave and pitch effects were considered by means of time varying restoring moment [20,21,22]. Basically, three analytical approaches were used in the present study.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical and Analytical Approaches for Roll Motion Analysis in Regular Longitudinal Waves

Peşman

Kolukısa

Taylan

2015

Polish Maritime Research

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In this study numerical and analytical approaches were investigated in terms of accuracy of their results, practicality of solution and ability to reproduce the main features of the parametric roll phenomenon such as loss of stability and bifurcations in parametric roll motion analysis of ships. In general, single-degree-of-freedom analytical approach is based on reducing number of degrees of freedom from 3 to 1 by using the quasi-static Froude-Krylov assumption, incorporating heave and pitch effects by means of a time varying restoring moment. On the other hand, numerical approaches to motion of six and four degrees of freedom are based on three dimensional diffraction

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Section: Description Of Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical and Analytical Approaches for Roll Motion Analysis in Regular Longitudinal Waves

Peşman

Kolukısa

Taylan

2015

Polish Maritime Research

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“…These approximations for the restoring moment make it possible to obtain analytical solutions for the parametric roll amplitude [2][3][4][5][6][7]. A harmonic-balance method [2], a multiple-scales method [3], and an averaging method [4][5][6] were used for obtaining analytical solutions in previous studies.…”

Section: Introductionmentioning

confidence: 99%

Averaging methods for estimating parametric roll in longitudinal and oblique waves

et al. 2017

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The International Maritime Organization is still developing second generation intact stability criteria for the roll motion of ships. For level 2 vulnerability criteria for parametric roll that require no expert knowledge about nonlinear dynamics, various analytical approaches are proposed in this study based on averaging methods. Firstly, an averaging method is applied to an uncoupled roll equation without fitting a polynomial to the calm-water GZ curve, thereby taking into account more accurate effect of the restoring arm. Secondly, the parametric roll amplitude is estimated more accurately using an averaging method that takes into account the effect of superharmonic roll motion. Thirdly, the critical speed for parametric roll is estimated, which is expected to reduce calculation processes in the design stage. Fourthly, the averaging method is extended to parametric roll in oblique waves, thereby taking into account the effect of both the ship's speed and course, which are helpful for an operational decision. Finally, the proposed analytical approaches are verified against an existing averaging method, numerical simulations, and free-running model experiments.

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Assessment of Ship Roll Damping Through Full Scale and Model Scale Experiments and Semi-empirical Methods

Söder

Rosén

Werner

et al. 2019

Contemporary Ideas on Ship Stability

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Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction

Cited by 23 publications

References 8 publications

Numerical and Analytical Approaches for Roll Motion Analysis in Regular Longitudinal Waves

Numerical and Analytical Approaches for Roll Motion Analysis in Regular Longitudinal Waves

Averaging methods for estimating parametric roll in longitudinal and oblique waves

Assessment of Ship Roll Damping Through Full Scale and Model Scale Experiments and Semi-empirical Methods

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