How do I solve fourth order PDE numerically?

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.

Answer 1

[Bill Greene]

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