207_add_Added Masses of Ship Structures.pdf - 196 5 Added Masses of Bodies Moving Close to a Free Surface Fig 5.22 Coordinate axes and notations for

207_add_Added Masses of Ship Structures.pdf - 196 5 Added...

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196 5 Added Masses of Bodies Moving Close to a Free Surface Fig. 5.22 Coordinate axes and notations for inclined ship frame For three types of bulb-shaped shipframes considered in Sect. 2.4 (see Fig. 2.50 ) they proposed the following formulas: Type I: λ 220 = π 2 ρb 2 s ; Type II: λ 220 = πρb 2 s 1 b 2 s 2 H 2 s ; Type III: λ 220 = π 2 ρb 2 s 2 . Under torsional oscillations of a hull vibrating on a free surface, the added mo- ment of inertia of shipframe with respect to the x -axis (which is directed along the axis of the ship and lies in the plane of waterline) can be found from formula λ 44 = 0 . 5 λ 44 , where λ 44 is the added moment of inertia of a duplicated contour under rotation around the same axis in an infinite fluid. If coefficients in the Lau- rent series of the function mapping the exterior of the contour to the interior of the unit disc are known, then λ 44 can be found using Sedov’s formulas [206], given in Chap. 2 .
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