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Vibrations problem - Deriving the natural frequencies

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data

    A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions

    2. Relevant equations

    Not sure

    3. The attempt at a solution

    I am really not sure how to start this one, can someone help please
     

    Attached Files:

    Last edited: Feb 15, 2010
  2. jcsd
  3. Feb 15, 2010 #2
    Try to use
    Flexural stiffness definition (EI=E*I/L),
    Hooke's law (F=-kx)
    Beam equation
    [tex]\frac{\partial^2}{\partial x^2}\left(EI \frac{\partial^2 u}{\partial x^2}\right) = w[/tex]
    , in the simple case
    [tex]EI \frac{d^4 u}{d x^4} = w(x)[/tex]

    See also http://en.wikipedia.org/wiki/Beam_equation
     
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