Abstract: A time domain analysis of the motion of a single point moored ship in regular and irregular waves is presented. Linear and nonlinear wave forces are calculated by the convolution integrals of the impulse response functions and wave elevations. 3-D panel method is applied to get the linear and quadratic frequency transfer functions of wave forces on the vessel. It is shown that the consideration of first and second order wave forces is important in the calculation of the slew motion(of a moored ship) in irregular waves.

　

 It is important to predict and control the excessive lateral motion of a moored ship in wind, waves or currents, to prevent the dredging of anchor or collision with other ships. Many researchers like Fujino [1], Obokata [2], Kijima [3] proposed the prediction and reduction methods of such motion. McWilliam et al [4] considered the first and second order wave forces on a single point moored ship. Jiang et al [5] calculated the motion of a single point moored tanker subjected to current, wind and waves. In this paper, the authors tried to calculate the effect of irregular waves, in the slew motion of a moored ship. At first, linear and quadratic frequency transfer functions of wave forces are calculated by 3-D panel method. These transfer functions are Fourier transformed to get the impulse response functions. Irregular waves are reproduced with use of ISSC spectrum, and the convolution integrals of irregular wave and impulse response function are carried out to get the wave forces in time domain. M.M.G maneuvering equations are used to simulate the motion of a ship[6]. Inoue [7] formulas are applied to predict the hull forces, and the tension of mooring line is calculated under catenary assumption.

　

 Surge, sway and yaw motion of a ship in regular or irregular waves are expressed by equation (1). Figure 1 shows the coordinate system and definition of each parameters.

　

　

　

 Here, the subscript H, WV, T means hull forces, wave forces and tension of mooing line. Hull force XH , YH, NH are predicted by the Inoue formulas, and the added masses and moments are gotten from the Motora chart [8].

　

 In this paper, KRISO 300K VLCC [9] is used for the calculation. On the Table 1, the principal particulars of the model are listed. 3-D panel method is applied to get the frequency transfer function of the linear and nonlinear wave forces on the model[10]. Figure 2 shows the mesh distribution for the model ship. Total 620 panels are distributed on the hull, and the boundary value problem to get the strengths of each sources on the panels is solved. Figure 3 is showing the frequency transfer functions of first order wave forces. Second order wave forces are calculated. considering relative wave elevation ζa, 1^st order velocity potential φ⁽¹⁾, and the rotation angle of the ship α.