# How to obtain w and Natural frequency as solution of unknown time function?

• Nov 4th 2011, 12:11 PM
derdack
How to obtain w and Natural frequency as solution of unknown time function?
I have a problem with decoupling this PDE. The solutions of time unknown function are natural frequencies. Is it possible t obtain it. I believe that the calculating w is smaller problem then obtaining the solutions of time function. If somebody from the physics can help for decoupling PDE and then calculating code for values.

Everything known constants. Unknown x, t.

I1[x_] := I0/(1 + C0/E^((2*\[Alpha]*(x - xc))/h));

Conditions:
w[0, t] = 0;
w[L, t] = 0;
D[w[0, t], {x, 2}] = 0;
D[w[L, t], {x, 2}] = 0;
D[w[x, 0], {t, 2}] = 0;
D[w[x, 0], {t, 2}] = 0;

PDE

D[E0*(I0 - I1[x])*w[x, t], {x, 4}] + \[Rho]*A*D[w[x, t], {t, 2}] == 0
• Nov 6th 2011, 04:25 AM
HallsofIvy
Re: How to obtain w and Natural frequency as solution of unknown time function?
I don't understand your notation. Is "D[f(x,t), {x,4}]" the fourth derivative of f with respect to x?
• Nov 6th 2011, 04:29 AM
derdack
Re: How to obtain w and Natural frequency as solution of unknown time function?
Yes, this is code in Mathematica.