Partially nonlinear time domain analysis on ship motions in waves with translating-pulsating source Green function

Abstract

The motion responses of ship in waves were investigated in time domain with both linear and partially nonlinear numerical method. The retardation functions that accounted for the memory effect were computed from transforms of frequency hydrodynamic data evaluated based on the Three Dimensional Translating-pulsating Source Green function (3DTP). Numerical simulations were carried out to validate the present linear method. It was found that the motion responses obtained from equations referenced to the equilibrium axis system indicate shifts when compared with the frequency domain results, especially for the pitch motion, while motion responses obtained from equations referenced to the body fixed axis system indicate satisfactory agreement with both the frequency domain results and experimental results. Then nonlinear incident wave forces and hydrostatic restoring forces were calculated on the instantaneous wet surface of hull. The contributions of the incident wave and the restoring forces on nonlinearity with increasing wave amplitude were analyzed for three vehicles with different hull forms. The results illustrates that the motion transfer functions of Wigley III hull see an upward trend at the resonant zone with the increasing wave amplitude, while those of S60 hull depict a downward trend and those of SWATH 6A remain almost constant.