关键词: 参数激励横摇, 窄带谱, 能量包线随机平均法, FPK方程

Abstract: The International Maritime Organization (IMO) developed the second generation of intact stability criteria, which includes the parametric rolling. In the direct stability assessment, numerical simulation is the most direct method to study the rolling response and stability. However, the analytical analysis method is still necessary because ship capsize is a rare event. The stochastic averaging method of energy envelope can accurately solve the random motion response under the excitation of white noise. However, real waves in the practical engineering correspond to a narrow-band spectrum. The research on the applicability of the stochastic averaging method shows that the system damping and the excitation intensity should be small enough and the excitation bandwidth should be large enough for the non-white noise excitation. An improved method of the stochastic averaging method of energy envelope under the narrow-band spectral excitation is studied based on the above situation. The phase angle is introduced into the original stochastic averaging method of energy envelope by referring to the standard stochastic averaging method. The nonlinear restoring force can be considered, and the limitation of the ideal white noise excitation required by the original method is relaxed to make it possible for the narrow-band excitation. The stationary probability density function (PDF) of the roll angle obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation agrees well with that of the Monte Carlo method. The improved stochastic averaging method of energy envelope can accurately calculate the rolling response of the ship under the excitation of real waves and evaluate the ship roll stability. It can provide guidance for the safe navigation of the ship.

Key words: parametric rolling, narrow-band spectrum, stochastic averaging method of energy envelope, Fokker-Planck-Kolmogorov (FPK) equation