Time-domain analysis of wave exciting forces on floating bodies at zero forward speed

The problem of determining the exciting forces acting on a rigid floating body due to uni-directional waves has been extensively studied. The problem is usually formulated in the frequency domain by assuming that the incident waves are sinusoidal of fixed frequency. Results for more general wave systems may then be found using superposition and Fourier analysis. In this paper, the problem will be formulated directly in the time domain. Numerical techniques are developed for bodies of arbitrary shape. The solutions in the time domain and frequency domain are related through the use of Fourier t ransforms. Time-domain analysis has been used by several authors to solve the radiation problem. For axisymmetric bodies, Newman I determined the impulse response functions for right circular cylinders of various radius to draft ratios. Beck and Liapis z and Liapis and Beck3 use the technique to solve the radiation problem for arbitrary three-dimensional bodies at zero speed and with forward speed respectively. The use of t ime-domain analysis to solve the exciting force problem has not been widely investigated. Wehausen 4 developed the analogue to the Haskind relations for zero forward speed in the time domain. Using these relations, the exciting force is determined as an integral over the body surface of combinations of the incident wave potential and the radiated wave potentials. The solution of the diffraction problem remains of interest because the Haskind integral relations cannot be used to calculate local phenomena such as wave elevations or hydrodynamic pressures. Direct solution of the diffracted wave problem in the time domain is interesting for several reasons. Possibly, the most important reason is that the method used here may be extended to the cases of steady forward speed and/or arbitrary maneuvers of the body without any serious modifications to the approach. To the contrary, frequency domain methods involve very difficult Green function evaluations at steady forward speed and are not meaningful for general transient maneuvers. The time domain approach is also very useful in verifying and clarifying the relationship between frequency domain results and time domain results. Frequency domain solutions are often used to develop time domain