Three Dimensional Effects on the Hydrodynamic Coefficients and Wave Exciting Forces Used in Predicting Motions of Ships

Abstract

The three_dimensional boundary value problem for the unsteady motion of a ship oscillating on the free surface is formulated for zero forward speed. Various forms of the integral equation methods are formulated. The three_dimen_sional source distribution method is developed to compute the added mass and damping coefficient and the wave exciting forces on a ship. &&The integral equation is solved approximately by three different methods: successive approximation by Neumann series, iterative method by use of infinite fluid solution and linear algebraic equations. The convergence of the iteration method is studied to discover why it does not converge for all frequency ranges. The improved iteration method by Buckner_Chertock series is applied for low frequency ranges to improve the convergence.&&The integral equation is shown to fail at the infinite number of discrete eigenfrequencies of the interior Dirichlet problem. The difficulty near these eigenfrequencies can be removed by using a new form of Green's function. The new Green function is constructed by adding an interior source to the fundamental Green's function. This form of the Green's function produces a new integral equation and removes the numerical difficulty near the eigenfrequencies. &&The strip theory is considered to be invalid for computing hydrodynamic coefficients and exciting forces due to short waves. Comparison of the results of strip theory with those of 3-D theory shows that for the low and extremely high frequencies of oscillation, strip theory gives a poor result to compute the added mass; however, strip theory is a good approximation for fairly high frequency. The 3-D effects on the wave exciting forces are investigated for the head sea. The axial distribution of the wave exciting forces are computed using the three dimensional theory, Haskind's formula, and a 2-D strip theory by Salvesen, Tuck, and Faltinsen (1970). The 3-D theory shows that greater forces occur near the bow than the stern for the head sea and decrease as the wave passes along the ship. This confirms Faltinsen's (1971) theory.