In this paper, we describe a new time-domain mathematical model by which the problem of a ship hull, as a 3-D body, moving at a constant speed and oscillating amongst sea waves, is solved. Perturbation caused by the ship motion is considered as a distribution of normal velocities on the reference wetted surface of the hull. Furthermore, the general normal velocity on the wetted surface is expressed as a finite series in terms of the incident wave potential and the geometry of the wetted surface. A precise linear decomposition for general normal velocity distribution on the wetted surface of an arbitrarily shaped hull is presented. This enables the body boundary conditions to be exactly fulfilled. Integral equations for the impulsive and memory part of the modal scattering potential due to radiation and diffraction potentials and their interactions are also deduced. Diffraction and radiation problems are considered simultaneously in the analysis. In this way the basic dichotomy of linear theory between radiation and diffraction problems is removed. The treatment also allows hydrodynamic forces to be calculated separately from the motions. No restrictions apply to the wave direction, and motion amplitudes can be large. To validate the mathematical model, three cases, including both radiation and diffraction, are investigated. Results of calculations are compared with experimental and theoretical results published elsewhere, and the comparison shows excellent agreement.
The problem of ship motion in waves has been studied extensively using frequency domain analysis (Bruce, 1990). For arbitrary motions, however, it is necessary to solve the problem in the time domain for a 3-D body that is moving at a constant forward speed and oscillating in waves. Linear time-domain analysis in the solution of the radiation problem for a body moving at a constant forward speed has been employed by Liapis (1985).