Stochastic dynamic analysis of rolling ship in random wave condition by using finite element method

Nonlinear stochastic rolling is a primary contributor to ship instability. Random wave excitation is described in this study as a combination of harmonic excitation and Gaussian white noise excitation, and the nonlinear rolling of a ship subjected to this composited excitation is investigated using stochastic vibration methodology and a numerical analysis approach. The Fokker-Planck (FP) equation for nonlinear stochastic ship rolling is derived, and the associated transient probability density function (PDF) is numerically solved by applying the finite element method (FEM) and Crank-Nicolson method, and the findings are manifested to be consistent with the Monte Carlo simulation (MCS). This proves the applicability and effectiveness of the FEM in the numerical study of the nonlinear stochastic ship rolling. Then the effects of harmonic excitation amplitude and stochastic excitation intensity in stable and unstable regions on nonlinear ship rolling are investigated, which provide essential references for ship stability and capsizing research.

Automated summary

This study investigates the nonlinear rolling of a ship under the combined excitation of harmonic excitation and Gaussian white noise excitation. The Fokker-Planck equation for nonlinear stochastic ship rolling is derived and numerically solved using the finite element method and Crank-Nicolson method. The findings are consistent with Monte Carlo simulation, demonstrating the applicability and effectiveness of the numerical methods used. The effects of harmonic excitation amplitude and stochastic excitation intensity on nonlinear ship rolling are also analyzed, providing important references for ship stability and capsizing research.