how to define Boundary conditions for a 4th order PDE?

Governing Equation =

w(x,t) = W(x)*sin(f*t)

w(x,t) deflection in the beam w.r.t time

W(x) = the sought mode shape

f = frequency or the natural frequency

After subsituting the "w(x,t) = W(x)*sin(f*t)" in the governing equation we get an ODE, but i want to directly solve it as a PDE

Boundary conditions i have to solve for are for when we get the ODE; so do i use the same B.C for the PDE too as i did for the ODE?

at x = 0 at x=L

It is a Guided-Guided Beam or a Sliding-Sliding beam, thats why the B.C are same at both ends

[Piotr Haciuk]

Hi, have you found the answer yet?