315_add_Added Masses of Ship Structures.pdf - 6.9 Added Masses at Complex Structure Motion Q2 = l/2 l/2 0 305 2 p(x t)f2(x)r 0 d dx where p(x t is the

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6.9 Added Masses at Complex Structure Motion 305 Q 2 = l/ 2 l/ 2 2 π 0 p Σ (x,θ,t)f 2 (x,θ)r 0 dθ dx, where p Σ (x,θ,t) is the total pressure on the shell and f 1 (x,θ) and f 2 (x,θ) are the respective relative displacements of the shell and the stiffeners. As a result, we obtain the shell equations of motion as the ones for a system with two degrees of freedom: M 11 ¨ q 1 + N 11 q 1 + M 21 ¨ q 2 + N 21 q 2 = P 1 , M 12 ¨ q 1 + N 12 q 1 + M 22 ¨ q 2 + N 22 q 2 = P 2 . In these equations, we have introduced the notation M 11 = 27 128 πρ 0 hr 0 l 1 + 8 27 + 1 ) ρr 0 ρ 0 h ; M 12 = M 21 = 3 8 πρ 0 hr 0 l 1 + β + 1 3 ρr 0 ρ 0 h ; M 22 = 3 4 πρ 0 hr 0 l 1 + F bh + β + 1 3 ρr 0 ρ 0 h ; C 11 = 3 4 π 5 1 + l 4 b 4 + 4 3 l 2 b 2 r 0 D l 3 + π 3 4 r 0 l T 1 + 3 2 l 2 b 2 T 2 ; C 12 = C 21 = π 5 r 0 D l 3 + π 3 r 0 4 l T 1 + 3 4 π 2 · l 2 r 2 0 T 2 ; C 22 = 2 π 5 EJr 0 bl 3 + π 3 r 0 2 l T 1 + 3 4 π 2 · l 2 r 2 0 T 2 ; P 1 = − 3 4 πρ 0 hr 0 l 1 + 2 3 ρr 0 ρ 0 h ¨ A ; P 2 = − πρ 0 hr 0 l 1 + F bh + ρr 0 ρ 0 h ¨ A, (6.81) where D is the cylindrical rigidity of the shell, h is the shell thickness, F the area

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• Fall '09
• Frequency, Shell, Interior, Lagrangian mechanics, B-2 Spirit

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