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Solving for Distributed Spring Work

  1. Apr 24, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to find the distributed spring work over a beam connected to a ceiling. The position on any point on the beam is given by Z = h + σ*(x-x_ea). The spring constant is K. This is a wing model, where h is the plunge, alpha is the pitch, and x is a position on the chord.

    2. Relevant equations
    Z = h + σ*(x-x_ea)
    Z_dot = h_dot + σ_dot*(x-x_ea)
    F = K*Z
    dZ = dh + dσ*(x-xea)

    3. The attempt at a solution
    This seems like a simple question, but, is the potential energy differential for the wing
    dW = ∫K*Z*dz = ∫K*Z*(dh + dσ*(x-xea))dx
    or can it simply be
    dW = 1/2*K*Z^2dx
    ?
     
  2. jcsd
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