MIT2_019S11_SK3 - 2.019 Design of Ocean Systems Lecture 7...

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2.019 Design of Ocean Systems Lecture 7 Seakeeping (III) February 25, 2011
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Motions and Wave Loads on a Barge A regular plane progressive incident wave in deep water travels along the x-direction: η I ( x, t )= a cos( ω t kx ) Φ I ( x, y, z, t ga e kz sin( ω t ) ω To find the wave force and motion of the barge in the vertical direction using long- wave and strip theory assumptions. z y x B D L Image by MIT OpenCourseWare.
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Heave Wave Excitation on a Barge (I) F E 3 = F I 3 + F D 3 Using the strip theory (which is valid for B/L << 1), we have: R L/ 2 R L/ 2 R L/ 2 F E 3 = L/ 2 f E 3 ( x )d x, F I 3 = L/ 2 f I 3 ( x )d x, F D 3 = L/ 2 f D 3 ( x )d x Froude Krylov force component: Z B/ 2 f I 3 ( x )= P I ( x ) n z d y 2 Z 2 = ( ρ Φ t ( x, y, z = D, t )d y 2 = B ρ ga e kD cos( ω t kx ) Z L/ 2 F E 3 = f E 3 ( x )d x L/ 2 Z L/ 2 = B ρ e cos( ω t )d x L/ 2 µ = ρ gaB 2 e sin kL cos ω t k 2 In the limit ω→ 0: F E 3 ρ gaBL cos ω t = ρ g η ( t )( BL )
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Heave Wave Excitation on a Barge (II) Long-wave assumption: wave motion is a flow slowly varying in space and time.
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MIT2_019S11_SK3 - 2.019 Design of Ocean Systems Lecture 7...

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