In this paper the path integral solution technique is applied to the motion of a ship in irregular waves. The exci ting moment due to the irregular waves is modeled as a non-white noise in this study. In the past, most appoaches to solve this problem yielded only limited information on the roll response statistics such as a mean square of the roll angle. Dunne has developed an approximate method for dealing with a nonlinear systems which are disturbed by non-white noise. He combined the method of equivalent linearization and the FPK technique to obtain some useful results. His method is based on the assumption that the crossing properties of the response can be approximately replaced by the excitation with a white-noise process of suitable intensity. Then they reinstated the nonlinear restoring function from the equivalent linearized equation of motion. The authors have developed new techniques based on the Dunne's method. The proposed scheme is capable of dealing with the full non linear damping and nonlinear restoring function with the equivalent white-noise intensity. The equivalent white-noise excited nonlinear equation of motion is solved by path integral solution technique to obtain the needed joint probability density function. The numerical results indicate that the proposed scheme is preferred over the existing method when the damping effects become dominant.
The present study investigates a method of predicting the threshold crossing time by solving a nonlinear rolling equation of motion of a ship in irregular waves. In the past, those approaches to solve this problem can be illustrated as an equivalent linear equation(Kaplan, 1966), a perturbation method(Flower,1976), and functional representation method(Hasselman,1966)(Vassilopoulos, 1967). But these yielded only limited information on the roll response statistics such as a mean square of the roll angle.
