Fundamental Frequency of a Membrane

jimjam91

Hey guys,

I've been looking for a formula to calculate the fundamental frequency of a plate under tension but i can't seem to find one that isn't for a string. I want to use the formula to find out the relationship between the tension and the frequency.

I have an approximate density and fairly accurate measurements of the area of the plate.

Any help with getting closer to an answer, even if it's very approximate, would be a real help.

If you need to know anything else about it to help, let me know.

Thanks in advance:)

jimjam91

I think i may have derived the formula but if anyone knows better, please correct me.

T=4f²LVρ or T=4f²L²DWρ

For which:

T=Tension
f=Frequency
L=Legnth (one dmension of the plate)
V=Volume
ρ=Density
W=Width (the other dimension)
D=Depth

I used the formula for a string to get this, i'm not sure if that's even the right sort of thing to do.

Reenakjr

Hi,

Frequency f for a given plate is proportional to the square root of the tension T.
F = k sqrt(T)

If F1 and T1 are the new frequency and tension:
F1 = k sqrt(T1)

F1 / F = sqrt(T1 / T)
T1 / T = (F1 / F)^2