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

315_add_Added Masses of Ship Structures.pdf - 6.9 Added...

This preview shows page 1 - 2 out of 2 pages.

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
Image of page 1

Subscribe to view the full document.

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

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes