Influence of Linear Filters and Nonlinear Damping Models on the Stochastic Roll Response of a Ship in Random Seas

Roll motion is the most critical ship motion leading to capsizing. The single-degree-of-freedom (SDOF) model is applied in order to simulate the roll motion in random beam seas. The random wave excitation term in the SDOF model is approximated by a second-order linear filter or more accurately, by a fourth-order linear filter as a filtered white noise process. Then the original SDOF model would be extended into a four-dimensional (4D) or a six-dimensional (6D) dynamic system, respectively. For the 4D coupled system, it can be viewed as a Markov system whose probability properties are governed by the corresponding Fokker-Planck equation. With the advantage of Markov property, the stochastic roll response can be obtained by the efficient 4D path integration (PI) method. The effect of different damping models, i.e. the linear-plus-quadratic damping (LPQD) model and linear-plus-cubic damping (LPCD) model, on the stochastic roll response is investigated. Furthermore, Monte Carlo simulation is introduced in order to validate the stochastic roll responses calculated by the 4D PI method as well as to study the influence of two different linear filter models on the response statistics.