# Accession Number:

## AD0692507

# Title:

## A RATIONAL STRIP THEORY OF SHIP MOTIONS: PART I.

# Descriptive Note:

## Interim technical rept. 1 Nov 68-28 Feb 69,

# Corporate Author:

## MICHIGAN UNIV ANN ARBOR DEPT OF NAVAL ARCHITECTURE AND MARINE ENGINEERING

# Personal Author(s):

# Report Date:

## 1969-03-01

# Pagination or Media Count:

## 105.0

# 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 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

# Descriptors:

# Subject Categories:

- Marine Engineering
- Fluid Mechanics