Resonant frequency of an annular ring? Hookes Law?

AI Thread Summary
The discussion focuses on determining the resonant frequency of an annular ring clamped at its outer diameter with a force applied at the inner diameter. The user seeks a general equation, suggesting that Hooke's Law may be relevant, along with factors like the ring's thickness and elastic modulus. They reference the resonant frequency formula for tuning forks, indicating a potential connection to their inquiry. Additionally, the user mentions the need for Bessel functions to analyze cylindrical harmonics, which are relevant in musical instrument acoustics. The complexity of the topic is acknowledged, with a hope for further insights from the community.
antsknee
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Hi,

I am trying to work out the resonant frequency of an annular ring, does anyone know a general equation for it?

For example the ring has an outside diameter = OD and inside diameter = ID. The ring is gently clamped at the outside diameter and a force F applied evenly at the inside diameter. At a particular frequency the amplitude of displacement will be maximum.

I believe it would be something like hookes law. The thickness of the ring would be a factor as well as the elastic modulus of the ring.

Thanks,

Anthony.

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I have been looking at tuning forks for inspiration.

The resonant frequency of a tuning fork is:

f=(1/l2)\sqrt{}(AE/p)

l=length of the prongs
A=area of prongs
E=youngs modulus of material
p=density of material

I will return with more thoughts as I have them.
 
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I have been searching these forums and it seems I need a Bessel function for cylindrical harmonics. They are used to understand musical instruments such as cymbals. The wikipedia page looks very complicated, I bet I won't get any replies to this thread :)

http://en.wikipedia.org/wiki/Bessel_function
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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