Mathematical Modeling of a Ship Motion in Waves under Coupled Motions

Aung Myat Thu, Ei Ei Htwe, Htay Htay Win

In this paper, research area is emphasized on motion of a ship due to anti- symmetric coupled motion of roll-yaw and sway-roll-yaw. This paper also expressed wave forces, hydrodynamic coefficients and 2-DOF and 3-DOF model of a surface vessel and its motions. The required hydrodynamic coefficients and wave forces are obtained from integration of sectional added-mass, damping and restoring coefficients, derived from Frank’s close-fit conformal mapping method. The governing equations for motion equations are solved numerically by using Runge-Kutta method. The vessel used in this analysis is monohull vessel type which is 28 m long. In the calculation of floating body motions, two-dimensional added mass, damping, and excitation for each ship sections are solved out. The governing equations comprised of second order ordinary differential equation that come from equation of hydrodynamic forces and external exciting forces. This paper describes the complete model of Tug and its numerical calculation solves with Matlab.