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# lect_9 - Six-Degree-of-Freedom Motion of a Ship in Waves...

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Six-Degree-of-Freedom Motion of a Ship in Waves Translation in x: surge η 1 (t); Translation in y: sway η 2 (t); Translation in z: heave η 3 (t); Rotation with x: roll η 4 (t); Rotation with y: pitch η 5 (t); Rotation with z: yaw η 6 (t);
Solution of Equation of Motion of a Ship in Waves Equation of Motion: In a state-sate, ship has a periodic response: the wave excitation: The equation of motion becomes: In a matrix form, it becomes: Thus, we have where The key is to determine the 6 × 6 matrices: added mass [A], damping [B], restoring coefficients [C], and 6 × 1 vector: excitation {f}

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2.29 - Numerical Fluid Mechanics Spring 2007 Lecture 9 - Uniform Flow Past an Arbitrary Body Dr.Yuming Liu U B x y n S 0 Φ ( x, y ) = - Ux + ϕ ( x, y ) On S B : Φ n = 0 -→ ϕ n = Un x In the fluid: 2 Φ = 0 -→ 2 ϕ = 0 In the far field: ϕ = 0 Purpose: To find ϕ ( x, y ) on the body surface ( S B ). After knowing ϕ on S B , flow velocity and pressure on S B can be determined easily. Apply Green’s Theorem -→ a boundary integral equation: Z S B ϕ ( ξ, η ) ∂G ∂n d ξη + π ϕ ( x, y ) = Z S B ϕ n ( ξ, η ) Gd ξη G ( x, y ; ξ, η ) = - ln p ( x - ξ ) 2 + ( y - η ) 2 To solve the above integral equation, we use the panel method.
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lect_9 - Six-Degree-of-Freedom Motion of a Ship in Waves...

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