Ballard, E.J., Hudson, D.A., Price, W.G. and Temarel, P.
Time domain simulation of symmetric ship motions in waves.
Transactions of the Royal Institution of Naval Architects, Part A: International Journal of Maritime Engineering, 145, (A2), .
A time domain mathematical model is presented for the prediction of heave and pitch motions in regular waves. In the linear model, the fluid forces and moments acting on a vessel are expressed in terms of convolution integrals, thus accounting for fluid memory effects. The required impulse response functions are obtained from transforms of frequency domain data evaluated using a three-dimensional potential flow analysis. These are referenced to both equilibrium and body fixed axis systems. Time domain simulations are performed using equations of motion referenced to both axis systems. Comparisons with frequency domain predictions show that the numerical implementation of the model referenced to a body fixed axis system is more accurate.
Subsequently, non-linear incident wave and restoring force/moment contributions are included in the mathematical model referenced to a body fixed axis system. These contributions are accounted for by considering the instantaneous underwater portion of the hull at each time step of the simulation. Predictions obtained from this partly non-linear model, for a range of wave amplitudes, are compared to both linear predictions and experimental results for two merchant ship hull forms.
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