A RATIONAL STRIP THEORY OF SHIP MOTIONS: PART I.
Interim technical rept. 1 Nov 68-28 Feb 69,
MICHIGAN UNIV ANN ARBOR DEPT OF NAVAL ARCHITECTURE AND MARINE ENGINEERING
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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 must be high. The hydrodynamic problem is then recast as a singular perturbation problem which is solved by the method of matched asymptotic expansions. 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 for this purpose. Author
- Marine Engineering
- Fluid Mechanics