The present study considers the nonlinear roll motion of containerships. The nonlinear wave excitation and restoring are applied for the ship motion, based on the assumption of weakly nonlinear ship motion. For the radiation component, an impulse response function (IRF) approach is applied. The nonlinear roll motions for a large containership and S175 hull are predicted in regular and irregular waves, and the results are compared with the results of a state-of-art program for nonlinear ship motion, called WISH. The effects of a few physical parameters on parametric roll motion are observed. The developed program is extended to creating polar diagram to predict nonlinear roll motion in various ocean conditions.


Roll motion of ships has been of great interest because it is the most important factor that affects stability and comfort of sailing. Since ships grow faster and larger in a recent decade, particularly in containerships, LNG carriers, and cruise ships, the nonlinearity of roll motion becomes a crucial element of large-ship design. Since the excitation of roll motion is transverse moment, large roll motion of symmetric ships has not been considered in head or following waves. However, many researches have proved the possibility of occurrence of very large roll angle in head or following waves when the wave encounter frequency is twice of roll natural frequency. This roll motion so called parametric roll is of great concern, nowadays. Strictly speaking, ‘parametric’ indicates the self-excitation or parametric excitation which can be used in Mathieu equation. Pauling and Rosenberg (1959) solved coupled heave-pitch-roll motion and showed the possibility of great roll angle in head or following waves. The researches at that point were based on the assumption that metacentric height, GM, varies in harmonic manner. However, GM variation is not harmonic in actual situation. So Dunwoody (1989) associated GM variation with spectrum. Large roll motion including parametric roll has significant nonlinearity.

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