Dynamic and first passage analysis of ship roll motion with inelastic impacts via path integration method

The inelastic impacts may happen in cold region and affect the stability of ship roll motions, which is worth studying in stochastic cases. This paper is devoted to analyzing the inelastic impacted ship roll motion under random wave excitations by path integration (PI) method. Ivanov non-smooth transformation is applied to combine impact condition and ship roll equation into one continuous equation; then, a further development on Gauss–Legendre path integration (GLPI) method is proposed. Moreover, a first passage type ship roll stability is studied based on path integration results. The stationary probability density function (PDF) is calculated in stable cases, while the first passage probability are carried out in unstable cases. The influences of different parameters on the stationary PDF and the ship roll stability are studied in this paper. The accuracy of our expended GLPI and solutions is verified by Monte Carlo simulation, which indicates that our improved PI method has wide prospect in application.