Determination of minimum required damping in stochastic following seas modeled by using Gaussian white noise

Abstract

Abstract The aim of this study is to present an analytical method to determine the minimum required damping moment for a stable ship in stochastic following seas modeled by using Gaussian white noise. Stochastic differential equation is used as a mathematical model to represent rolling motion of a ship. First, the minimum required damping is obtained analytically by using Lyapunov function. Second, analytically obtained damping values are verified by integrating the nonlinear stochastic rolling motion equation by stochastic Euler method (Euler–Maruyama Schema) to deduce whether rolling motion is stable or not. It can be seen from the results of numerical computation that the ship is sufficiently stable for the minimum required damping value obtained by the use of Lyapunov function and the minimum required damping is highly dependent on natural frequency of roll, diffusion constant and maximum variation of initial metacentric height.