Ship Roll Behaviour in Large Amplitude Beam Waves

Abstract

In this paper, the Homotopy Analysis Method (HAM) is applied to obtain high accuracy series solutions of roll motions of a ship, which encounters a nonlinear wave of large amplitude. Comparisons are made between roll responses in linear and nonlinear beam waves with identical wave slope and frequency. Furthermore, Floquet theory is applied to analyze the stability of HAM series solutions. Besides that, numerical simulation is used to verify the analytical solution and study the behaviors of the system under disturbance. All the results demonstrate that the proposed scheme is an effective analytic technique to study nonlinear ship rolling equation, and the stability analysis reveals the significance of researching ship roll motion in large amplitude nonlinear wave.