Time-Domain Analysis of Ship Motions.

Abstract

Linear time-domain analysis is used to model the flow created by small unsteady motions of a floating body moving at a constant forward speed in otherwise calm water. The hydrodynamic forces acting on the body are expressed in terms of convolution integrals of the arbitrary motion with an impulse response function. The impulse response function is defined as the potential due to an impulsive velocity (a step change in displacement). By using the method of singularity distributions, the problem of calculating the impulse response is reduced to solving a set of Fredholm equations of the second kind. The integral equations are solved numerically for bodies of arbitrary shape using a panel method. One of the integral equations must be solved by time stepping, but the kernel matrix is the same at each time step and is closely related to the kernel matrix used to solve the time independent integral equations. The added mass and damping in the frequency domain is found by Fourier-transforming the time-domain solution. Numerical results for the special case of zero forward speed are obtained for a sphere in heave and sway, a cylinder in heave and a Series 60 ship. The method has been also applied to the case of a ship moving at a constant forward speed. Comparisons are shown between the results of the present calculations to the more conventional frequency-domain calculations. Theoretical predictions and experimental results for the heave motion of a sphere released from an initial displacement are also given. In all cases, the comparisons are very good.