Stochastic roll response for a vessel with nonlinear damping models and steady heeling angles in random beam seas

Loss of ship stability is most frequently associated with extreme roll motion. For the case of random beam sea, a single-degree-of-freedom (SDOF) model is applied in the present study in order to represent the stochastic rolling behavior. The random wave excitation term in the SDOF model is approximated as a filtered white noise process by applying a second order linear filter. Accordingly, the original SDOF model is extended into a four-dimensional (4D) dynamic system. The coupled dynamic system can be viewed as a Markov system whose probabilistic properties are governed by the corresponding Fokker-Planck equation. Based on the convenient Markov property, a host of useful response statistics can be obtained by an efficient path integration (PI) method. Different nonlinear damping models, i.e. the linear-plus-quadratic damping (LPQD) model and the linear-plus-cubic damping (LPCD) model, and their effects on the stochastic roll response are investigated and the influence of the steady heeling angle on the response level associated with ship rolling in random seas is also studied. Furthermore, the accuracy of the response statistics computed by the PI technique is verified by means of the versatile Monte Carlo simulation (MCS) technique.