217_add_Added Masses of Ship Structures.pdf - 206 5 Added Masses of Bodies Moving Close to a Free Surface Fig 5.28 Coordinate axes and notations for a

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206 5 Added Masses of Bodies Moving Close to a Free Surface Fig. 5.28 Coordinate axes and notations for a floating cylinder For a circular cylinder of radius a we get from formulas ( 5.31 ): λ 33 = ρπa 2 / 2, λ 44 = 0. For a flat plate of width 2 a placed at the water surface we get from the same formulas: λ 33 = 1 2 ρπa 2 , λ 44 = 1 16 ρπa 4 . If a circular cylinder of radius R is floating on a surface of an infinite fluid, being immersed to depth H (Fig. 5.28 ), then its added mass per unit of length is expressed by the following formula [67]: λ 33 = ρR 2 π sin 2 α 6 k 2 ( 1 + 2 k 2 ) α + 1 2 sin2 α , where α is 1 / 2 of the angle of the immersed arc of the circle; k = 1 α/π ; h = R( 1 cos α) . If the cylinder is completely immersed ( α = π , H = 2 R , k = 0) then λ 33 = πρR 2 π 2 6 1 . Half-immersed cylinder ( α = π/ 2, k = 0 . 5) has added mass λ 33 = 0 . 5 πR 2 ρ . Dependence of the added masses λ 11 and λ 33 on the oscillation frequency of a floating cylinder for different values of α are given in [53, 87]. Typically in the

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• Fall '09
• Frequency, free surface, coordinate axes, vertical impact

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