Find Fundamental Frequency of Vibrating Mylar Membrane

[FrankCashio]

Alright I've been going crazy with this problem. I'm building an electrostatic loudspeaker. In order to get it right I need to find the Fundamental frequency of the vibrating membrane.

This membrane will be of an elastic substance, Mylar. Approx. 5 microns think with a young's modulus of about 4 GPA.

How do you go about solving a problem like this?

I know the solution will have tension, elasticity in the equation. I guess what I'm really asking is what are the group of equations defining modes of vibrations in elastic membranes. I know it will be in the form of a simple harmonic motion

f= 1/2 PI * SQRT(k/m) but there is nothing in that equation relating the restoring force of the membrane due to it's elasticity nor the effects of Air damping it due to drag/viscosity.

 

[nasu]

For a circular membrane with fixed rim the frequencies for resonance are given by
f_nm=j_nm*c/(2PI R)
where R is the radius of the membrane and j_nm are the zeroes of the Bessel function of first order.
The lowest value for j_nm in my table is 2.4
So this will give the lowest frequency.
You still need the speed of sound in your material (c).

 

[FrankCashio]

Oh sorry it would be a rectangle.

 

[nasu]

For rectangular, with same fixed rim conditions,
f_nm=(c/2)*[(n/Lx)^2+(m/Ly)^2]^(1/2)
(you take square root from the straight bracket)

Fundamental freq is for n=m=1
Lx,Ly - dimensions of the membrane