MIT2_019S11_SK4

# MIT2_019S11_SK4 - 2.019 Design of Ocean Systems Lecture 8...

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2.019 Design of Ocean Systems Lecture 8 Seakeeping (IV) March 4, 2011

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General Response of A Floating Body in Regular Ambient Waves ζ 3 ( t ) = <{ ¯ i ω t ζ 3 e } ζ 6 e Incident wave: z ζ 6 ( t ) = <{ ¯ i ω t } x Φ tt + g Φ z = 0 η ( t ) = Φ t /g ζ 5 ( t ) = <{ ¯ ζ 5 e } η I = a cos( ω t kx ) y ζ 2 ( t ) = <{ ζ ¯ 2 e i i ω ω t t } ζ 1 e ~n ζ 1 ( t ) = <{ ζ ¯ 4 e i i ω ω t t } ζ 4 ( t ) = <{ ¯ } 6 X Equation of motion: [( M j` + A j` ) ζ ¨ ` + B j` ζ ˙ ` + C j` ζ ` ] = F ¯ Ej e i ω t ( j = 1 , . . . , 6) (1) ` =1 6 X [ ω 2 ( M j` + A j` ) + i ω B j` + C j` ] ζ ¯ j = F Ej ( j = 1 , . . . , 6) ` =1 M j` : 6 × 6 elements of the egeneralized mass matrix A j` , B j` : 6 × 6 elements of added mass and wave damping matrices C j` : 6 × 6 elements of hydrostatic restoring matrix F Ej : 6 elements of the wave excitation vector ¯ Transfer function or Response Amplitude Operator (RAO): H j ( ω ) = ζ j a ( ω ) ( j = 1 , . . . , 6)
Numerical Method for Potential-Flow Problems Uniform free stream : Φ = Ux u = U, v = 0 , w = 0 2D point source : u r Φ = m 2 π ln x 2 + z 2 = m 2 π ln r m u r = 2 π r 2D point source plus point sink : Φ = m 2 π ln p ( x + s ) 2 + z 2 p m ( x s ) 2 + z 2 ln 2 π source sink

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