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. •The nonlinear rolling motion of a ship under combination excitation of harmonic and Gaussian white noise is investigated.•The Fokker-Planck equation and transient probability density function of the ship rolling are established and numerically solved by using the finite element method and the Crank-Nicolson method.•The numerical results agree well with the Monte Carlo simulation, indicating the accuracy and reliability of the finite element method.•The effects of harmonic amplitude and white noise intensity on ship rolling are next explored. The findings show that the greater the amplitude of harmonic excitation or the intensity of white noise, the more prone the ship rolling motion is to random jump. With some uncertain circumstances, the ship may lose stability or even capsize.