How do I solve fourth order PDE numerically?

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I am trying to solve the beam equation ρA(∂^2y/∂t^2) + EI(∂^4y/∂x^4)+ P(∂^2y/∂x^2) = 0 with the following boundary conditions:
  1. y(0,t) = 0
  2. ∂y/∂x(0,t) = 0
  3. ∂^2y/∂x^2(L,t) = 0
  4. ∂^3y/∂x^3(L,t) = 0
where x ∈ [0,L] and ρ, A, E, I, P are constants.

Accepted Answer

Bill Greene
Bill Greene on 24 Jul 2018
I have created an example, which might be of help, showing how to use the pdepe function to solve the beam equation : pdepe beam dynamics

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