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Math Help - Applied Math: Beam Deflection using Separation of Variables

  1. #1
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    Applied Math: Beam Deflection using Separation of Variables

    Beam's dynamic deflection is governed by the following PDE

    EI(∂^4w/∂x^4)+(rho)*A* (∂^2w/∂t^2)=f(x,t)

    where E = the modulus of elasticity, I = the moment of inertia, p = mass density, A = cross-section area, w(x,t) = deflection, 0 ≤ x ≤ L = axial coordinate, L = length, t = time. The load is given as the following function

    f(x,t) = sin(pi*x/L)sin(omega*t)

    Use separation of variable and the normal mode approach to find w(x,t) if the boundary conditions are

    w = 0 at x = 0 and x = L;

    ∂^2w/∂x^2=0

    And the initial conditions read w=O,

    ∂w/∂t =0 at t =0
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    Last edited by sublim25; May 11th 2011 at 10:56 AM.
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  2. #2
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    Write w(x,t)=F(x)T(t) and sub in to pde.
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