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r10_froudekrylov

r10_froudekrylov - 13.42 Spring 2005 13.42 Design...

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13.42 Spring 2005 13.42 Design Principles for Ocean Vehicles Prof. A.H. Techet Spring 2005 Froude Krylov Excitation Force 1. Radiation and Diffraction Potentials The total potential is a linear superposition of the incident, diffraction, and radiation potentials, ω φ = ( φ φ + φ ) e . (1) I + D R i t The radiation potential is comprised of six components due to the motions in the six directions, 1 2 3 4 5 6 th φ j where j = , , , , , . Each function φ j is the potential resulting from a unit motion in j direction for a body floating in a quiescent fluid. The resulting body boundary condition follows from lecture 15: ω 1 2 3) (2) φ j = i n j ; ( j = , , n ω ( , , φ j = i r G × n ± ) j 3 ; ( j = 4 5 6) (3) n G r = ( x y z ) (4) , , n n j ( j = , , ± = 1 2 3) = ( n , n y , n ) (5) x z In order to meet all the boundary conditions we must have waves that radiate away from the body. ikx Thus φ j e as x → ± ∞ . For the diffraction problem we know that the derivative of the total potential (here the incident potential plus the diffraction potential without consideration of the radiation potential) normal to the body surface is zero on the body: φ T = 0 on S , where φ = φ φ . n B T I + D version 1.0 updated 3/29/2005 -1- 2005, aht

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13.42 Spring 2005 φ I φ D ; on S (6) n = − n B We have so far talked primarily about the incident potential. The formulation of the incident potential is straight forward from the boundary value problem (BVP) setup in lecture 15. There exist several viable forms of this potential function each are essentially a phase shifted version of another. The diffraction potential can also be found in the same fashion using the BVP for the diffraction potential with the appropriate boundary condition on the body. This potential can be
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