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 ) ζ ¨ ` + B ζ ˙ ` + C ζ ` ]= F ¯ Ej e i ω t ( j =1 ,..., 6) (1) ` =1 6 X [ ω 2 ( M + A )+ i ω B + C ] ζ ¯ j = F ( j 6) ` =1 M :6 × 6 elements of the egeneralized mass matrix A ,B × 6 elements of added mass and wave damping matrices C × 6 elements of hydrostatic restoring matrix F : 6 elements of the excitation vector ¯ Transfer function or Response Amplitude Operator (RAO): H j ( ω ζ j a ( ω ) ( j 6)
Numerical Method for Potential-Flow Problems Uniform free stream : Φ = Ux u = U,v =0 ,w 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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2D doublet or dipole : source + sink, as s 0 while keeping 2 ms = µ .
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.019 taught by Professor Yumingliu during the Spring '11 term at MIT.

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

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