Nonlinear oscillations, dynamical systems, and bifurcations of vector fields : John Guckenheimer and Philip Holmes Springer-Verlag, New York, 1983, 453 pp., $32.00

Nonlinear parametric rolling in regular waves—a general procedure for the analytical approximation of the GZ curve and its use in time domain simulations

Influence of non-linearities on the limits of stability of ships rolling in head seas

http://www.tara.tcd.ie/bitstream/handle/2262/74878/Tarrant%20and%20Meskell%202016_preprint.pdf;sequence=1

Investigation on Parametrically Excited Motions of Point Absorbers in Regular Waves

This paper summarizes the results and the problems still open regarding the development of a 1.5DOF nonlinear mathematical model of the parametric rolling in longitudinal waves with particular regard to the head sea condition. A first part is devoted to the case of regular waves, while the second concerns parametric rolling generated by irregular waves obtained by means of white noise filtered through a linear filter with adjustable bandwidth and by using a Bretschneider spectrum. The availability of an extensive series of test results on scale models conducted at University of Trieste and at INSEAN, allows a thorough discussion of the problems connected with the threshold formulation for parametric rolling and its amplitude modelling above threshold.

/pdf/on-the-nonlinear-modeling-of-parametric-rolling-in-regular-4satdlt3r5.pdf

On the nonlinear modeling of parametric rolling in regular and irregular waves

This paper describes latest collaborative researches between Japan and the UK on parametric roll resonance of a container ship in following and head seas with realistic modelling of restoring moment as a nonlinear function of wave steepness in experimental, geometrical and analytical approaches. Firstly, captive model experiments were conducted, and demonstrated that the Froude-Krylov prediction could overestimate the amplitude of its variation. Secondly, Poincare mapping technique applied to the numerical model with measured time-varying restoring moment was used for tracing stable steady states, and revealed symmetry-breaking, period-doubling, chaos and capsizing associated with parametric roll resonance. Thirdly, an averaging method was applied to the same numerical model, and confirmed good agreement with the Poincare mapping as well as subcritical bifurcation. Finally, by utilising the present numerical model and methodology, it is shown that a requirement of higher metacentric height does not always improve safety for capsizing associated with parametric roll resonance.

/pdf/nonlinear-dynamics-on-parametric-roll-resonance-with-42r6ggrg4b.pdf

Nonlinear dynamics on parametric roll resonance with realistic numerical modelling

Comparison of North European and Japanese Purse Seiners by Capsizing Model Experiments

It is essential for realising risk-based design or performance-based criteria to establish theoretical modelling of extreme behaviours of an intact ship in waves up to capsizing. For this purpose, this paper summarises latest progresses in the researches conducted by the authors at Osaka University for improving theoretical modelling of intact stability in waves. Firstly, the methodology for calculating capsizing probability in beam wind and waves with piece-wise linear assumption is examined. Here a new formula covering both capsizing towards windward and leeward directions is provided. Secondly, for calculating restoring moment in longitudinal waves with sufficient accuracy, a hydrodynamic prediction method with wave-making and lifting components taken into account is proposed, and is reasonably well compared with captive model tests of a post Panamax container ship in head and following waves. This can be used in place of the Froude-Krylov prediction or captive tests for assessing the danger of parametric rolling for a practical purpose.Thirdly, for more efficiently identifying dangerous conditions in following and quartering waves, a numerical method for determining a heteroclinic bifurcation is proposed with its successful example to applied to surf riding thresholds with nonlinear factors taken into account.

Shinichi Urano

Papers

Nonlinear dynamics on parametric roll resonance with realistic numerical modelling

Comparison of North European and Japanese Purse Seiners by Capsizing Model Experiments

Some Remarks on Theoretical Modelling of Intact Stability