A Rational Strip Theory of Ship Motions: Part I

Abstract

The exact ideal_fluid boundary-value problem is formulated for a ship forced to heave and pitch sinusoidally in otherwise calm water. This problem is then simplified by applying three restrictions: 1) the body must be slender; 2) the motions must be small in amplitude compared with ship beam or draft; 3) the frequency of oscillation, w , must be high, viz., w= O(e-1/2), where e is the slenderness parameter. The hydrodynamic problem is then recast as a singular perturbation problem which is solved to order de2 by the method of matched asymptotic expansions. ( d is a motion_amplitude parameter.) Formulas are derived for the hydrodynamic heave force and pitch moment, from which added-mass and damping coefficients can be easily obtained. The latter are similar but not identical to those used in several other versions of "strip theory;" in particular, the forward_speed effects have the symmetry required by the theorem of Timman and Newman, a result which has not been realized in previous versions of strip theory. In order to calculate the coefficients by the formulas derived, it is necessary to solve numerically a set of boundary-value problems in two dimensions, namely, the problem of a cylinder oscillating vertically in the free surface. At least two practical procedures are available to this purpose.