• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.53-64
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• 2011

The present study considers multi-level approach for the analysis of parametric roll phenomena. Three kinds of computation method, GM variation, impulse response function (IRF), and Rankine panel method, are applied for the multi-level approach. IRF and Rankine panel method are based on the weakly nonlinear formulation which includes nonlinear Froude-Krylov and restoring forces. In the computation result of parametric roll occurrence test in regular waves, IRF and Rankine panel method show similar tendency. Although the GM variation approach predicts the occurrence of parametric roll at twice roll natural frequency, its frequency criteria shows a little difference. Nonlinear roll motion in bichromatic wave is also considered in this study. To prove the unstable roll motion in bichromatic waves, theoretical and numerical approaches are applied. The occurrence of parametric roll is theoretically examined by introducing the quasi-periodic Mathieu equation. Instability criteria are well predicted from stability analysis in theoretical approach. From the Fourier analysis, it has been verified that difference-frequency effects create the unstable roll motion. The occurrence of unstable roll motion in bichromatic wave is also observed in the experiment.

• Journal of the Society of Naval Architects of Korea
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• v.49 no.1
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• pp.60-67
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• 2012

This study considers the numerical analysis on parametric roll for container ships. As a method of numerical simulation, an impulse-response-function approach is applied in time domain. A systematic study is carried out for the parametric roll of two container ships, particularly observing the sensitivity of computational results to some parameters which can affect the analysis of parametric roll. The parameters to be considered are metacentric height (GM), simulation time window, and the discretization of wave spectrum. Based on the result of parametric roll simulation, numerical sensitivity and uncertainty in computational analysis are discussed.

• Ocean Systems Engineering
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• v.2 no.4
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• pp.239-255
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• 2012

Analysis of ship parametric roll has generally been restricted to simple analytical models and sophisticated time domain simulations. Simple analytical models do not capture all the critical dynamics while time-domain simulations are often time consuming to implement. The model presented in this paper captures the essential dynamics of the system without over simplification. This work incorporates various important aspects of the system and assesses the significance of including or ignoring these aspects. Special consideration is given to the fact that a hull form asymmetric about the design waterline would not lead to a perfectly harmonic variation in metacentric height. Many of the previous works on parametric roll make the assumption of linearized and harmonic behaviour of the time-varying restoring arm or metacentric height. This assumption enables modelling the roll motion as a Mathieu equation. This paper provides a critical assessment of this assumption and suggests modelling the roll motion as a Hills equation. Also the effects of non-linear damping are included to evaluate its effect on the bounded parametric roll amplitude in a simplified manner.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.3
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• pp.187-197
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• 2015

This study aims the development of a semi-analytic method for the parametric roll of large containerships advancing in longitudinal waves. A 1.5 Degree-of-Freedom(DOF) model is proposed to account the change of transverse stability induced by wave elevations and vertical motions (heave and pitch). By approximating the nonlinearity of restoring moment at large heel angles, the magnitude of roll amplitude is predicted as well as susceptibility check for parametric roll occurrence. In order to increase the accuracy of the prediction, the relationship between righting arm(GZ) and metacentric height(GM) is examined in the presence of incident waves, and then a new formula is proposed. Based on the linear approximation of the mean and first harmonic component of GM, the equation of parametric roll in irregular wave excitations is introduced, and the computational results of the proposed model are validated by comparing those of weakly nonlinear simulation based on an impulse-response-function method combined with strip theory. The present semi-analytic doesn’ t require heavy computational effort, so that it is very efficient particularly when numerous sea conditions for the analysis of parametric roll should be considered.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.3
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• pp.227-241
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• 2017

In this study, a Volterra system for the variations of metacentric height (GM) in waves is employed to simulate the parametric roll phenomena of ships in head sea condition. Using the present Volterra system, the transfer function of each harmonic component in the GM variation is computed for different ship models, including mathematical models and a real containership, and the results are validated through the comparison with the values obtained using the direct calculations based on a weakly nonlinear time-domain method. Then, a semi-analytic approach employing a 1-degree of freedom equation for roll motion is developed to simulate the parametric roll motions in irregular waves. In the derived approach, the nonlinear and time-varying restoring forces in the waves are approximated using the Volterra system. Through simulations of the parametric roll for different sea states, the effects of the 1st and 2nd-order harmonic components of the variations in the occurrence and amplitude of the parametric roll motions are investigated. Because of the strong nonlinearities in the phenomena, a stochastic analysis is conducted to examine the statistical properties of the roll motions in consideration of the sensitivities and uncertainties in the computations.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.3
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• pp.119-126
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• 2010

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.

• Journal of Ocean Engineering and Technology
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• v.34 no.2
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• pp.55-65
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• 2020

A review of the 2nd generation of intact stability by the International Maritime Organization is performed. The main issues with the new stability criteria are reviewed. In particular, the physical background and related mathematical formulations of the pure loss of stability and parametric roll are summarized. Based on a literature review, benchmark calculation results for 17 different types of ships are discussed, and the final results are in excellent agreement with our physical expectations. Some relatively serious design problems are found in the application of the new stability criteria to sample ships built in Korea, and possible technical solutions are proposed, which have to be improved in the coming years.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.4
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• pp.409-421
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• 2016

Container ships are prone to move at a greater speed compared to other merchant ships. The slenderness of the hull of container vessel is for better speed, but it leads to unfavorable motions. The pitch and roll are related and sometimes the vessel might be forced to parametric roll condition which is very dangerous. A fin attached to the ship hull proves to be more efficient in controlling the pitch. The fin is fitted at a lowest possible location of the hull surface and it is at the bow part of the ship. Simulations are done using proven software package ANSYS AQWA and the results are compared. Simulations are done for both regular and irregular seas and the effect of fin on ship motion is studied. P-M spectrum is considered for various sea states.

• Ocean Systems Engineering
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• v.4 no.2
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• pp.117-136
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• 2014

The increased interest in the design of energy efficient ships post IMO regulation on enforcing EEDI has encouraged researchers to reevaluate the numerical methods in predicting important hull design parameters. The prediction of added resistance and stability of ships in the rough sea environment dictates selection of ship hulls. A 3D panel method based on Green function is developed for vessel motion prediction. The effects of parametric instability are also investigated using the Volterra series approach to model the hydrostatic variation due to ship motions. The added resistance is calculated using the near field pressure integration method.

• Ocean Systems Engineering
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• v.11 no.4
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• pp.301-312
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• 2021

An optimization framework has been established and applied to a shipshape parametric FPSO hull design. A single point moored (SPM) shipshape floating system suffers a significant level of the roll motion in both the wave frequencies and low wave frequencies, which presents a coupling effect with the horizontal weathervane motion. To guarantee the security of the operating instruments installed onboard, a parametric hull design of an FPSO has been optimized with improved hydrodynamics performance. With the optimized parameters of the various hull stations' longitudinal locations, the optimization through Genetic Algorithms (GAs) has been proven to provide a significantly reduced level of the 1st-order and 2nd-order roll motion. This work presents a meaningful framework as a reference in the process of an SPM shipshape floating system's design.