Time domain ship motion based on 3D Transient Green's Function method (3DTGF) is established, in which the impulse response theory is employed and the memory effect part of hydrodynamic forces is solved by 3DTGF incorporated with high-order boundary element method (HOBEM). The motions of Wigley-III hull advancing at various speeds in waves are calculated by this method, the numerical results are validated with experiment data and they are in good agreement. High efficiency is observed in two stages that, the impulse response function is fit for waves exciting forces at any frequency in solving time motion equation, and 3DTGF method avoids free surface meshes in solving the time domain radiation and diffraction problems. It also shows the accuracy of the spatial distribution of velocity potential is improved by use of HOBEM.

The time domain ship motion equation is extended for partly taking nonlinear effect of wave forces into consideration, nonlinear Froude-Krylov forces and nonlinear restoring forces on instantaneous wetted surface as well as non-linear viscous damping are computed coinciding with time domain ship motions. The simulation results are more reasonable than linear method. A container ship motions with parametric roll occurring are simulated and analyzed by this weak non-linear method. Based on the theoretical model, computational code is developed. The parametric rolling of the container ship is investigated and the effect of wave height, wave length, ship speed, and the relation between frequency and roll nature frequency in regular waves are discussed. The threshold boundaries for parametric rolling are discussed.


Ship motions in waves is an important study area of the sea-keeping research. Numerical methods for research conclude strip theory, threedimension frequency domain methods, three-dimension time domain methods. In condition that the ship hull is thin with low speed, the strip theory can calculate the motion and force accurately. But this method neglects the three dimension effect of hydrodynamic and cannot be applied for ships with high speed or marine structures with complex geometry. Three dimension frequency domain methods are widely used in engineering practice, but the calculation is based on the assumption that the motion of ship hull is steady, so nonlinear effect cannot be considered. So three dimension time domain method is an important direction for research.

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