Lehrstuhl fürModellierung und Simulation

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Strip theory(Material is taken fromhttp://www.amarcon.com/fileadmin/user_upload/Documentation/1370-StripTheory-03.pdf)

Assumptions Strip theory considers a ship to be made up of a finite number of

transverse two dimensional slices, which are rigidly connected to each other.

Each slice is treated hydrodynamically as if it is a segment of an infinitely long floating cylinder;

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• All waves which are produced by the oscillating ship (hydromechanic loads) and the diffracted waves (wave loads) are assumed to travel parallel to the (y, z )-plane - of the ship.

• The fore and aft side of the body (such as a pontoon) does not produce waves in the x -direction.

• For the zero forward speed case, interactions between the cross sections are ignored.

UNIVERSITY OF ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Assumptions

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Strip theory is valid for long and slender bodies only.

In spite of this restriction, experiments have shown that strip theory can be applied successfully for floating bodies with a length to breadth ratio larger than three, , at least from a practical point of view.

/ 3L B

UNIVERSITY OF ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Assumptions

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The appearance of two-dimensional surge forces seems strange here. Then, the 2-D hydrodynamic sway coefficients of this equivalent cross section are translatedto 2-D hydrodynamic surge coefficients by an empirical method based ontheoretical results from three-dimensional calculations and these coefficients areused to determine 2-D loads

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Assumptions

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Account for the ship velocity

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Force representation

Ordinary strip theory by Korvin-Kroukovsky & Jacobs

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The two-dimensional nature of the problem implies three degrees of freedom of motion:• vertical or heave,• horizontal or sway and • rotational about a horizontal axis or roll.

The following assumptions are made:• the fluid is incompressible and inviscid,• the effects of surface tension are negligible,• the fluid is irrotational and• the motion amplitudes and velocities are small enough that

all but the linear terms of the free-surface condition, the kinematic boundary condition on the cylinder and the Bernoulli equation may be neglected.

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Mathematical problem formulation

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Mathematical problem formulation

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Mathematical problem formulation

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Frank‘s method of pulsating sources

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Frank‘s method of pulsating sources

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Frank‘s method of pulsating sources

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Frank‘s method of pulsating sources

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Frank‘s method of pulsating sources