Tuning forks, and symmetric structures

[GregLocock]

A few questions, some of which I know the answer to, others I don't.

1) Why does a tuning fork have two prongs rather than one (or I suppose three)?

2) Is the dominant resonant mode anti symmetric (cantilevers swaying in phase) or symmetric (prongs clapping)?

3) How does the tuning fork 'select' the mode from (2) as the dominant mode?

4) Does anyone have a classical tuning fork? If so could they post a good quality wav file of the complete excitation/decay cycle?

http://www.tms.org/pubs/journals/JOM/0511/Burleigh-0511.html

is somewhat relevant, I know. I don't like that wav file!

5) if we were to strike just one prong why does the other prong not behave as a harmonic absorber for the first prong (this is really a more general question about symmetrical modes)?










Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

The thing that bothered me about the single prong was that I was looking at the frequency at the window title. So I couldn't figure out whether:
1 - You were modeling a single prong - if so why was the frequency the same.
2 - You were attempting to model a double prong by using single prong with symmetry conditions - if so why didn't the deflection shape reflect the symmetry.

Now I know it is single prong, and the frequency is not the same. I am un-confused (relatively speaking)



=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

By the way, where is the table hiding?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[GregLocock]

In my head. I'll do it tonight.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MikeHalloran]

I'd be curious to see the modes that are not in the major plane of symmetry.



Mike Halloran
Pembroke Pines, FL, USA

 

[GregLocock]

Confession time: I used a single layer of 4 node plate elements, so an even larger pinch of salt is needed for the torsional behaviour of the system.

I'm loathe to model this properly in Hypermesh unless I have good dimensions to work to, which I've been singularly unsuccessful in finding.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MikeHalloran]

Dimensions for three forks in this paper:

http://www.kettering.edu/~drussell/Publications/TuningFork.pdf

Mike Halloran
Pembroke Pines, FL, USA

 

[MikeHalloran]

This article includes an equation, written in some ?ML that is coming up garbled in my browser:

http://wapedia.mobi/en/Tuning_fork

Mike Halloran
Pembroke Pines, FL, USA

 

[SomptingGuy]

What a great discussion. I just googled for natural modes of tuning forks and got a hit that confirms all the above.

One thing nobody has mentioned is that when you have a singing tuning fork you can presetnt it gradually to a hard surface like a table. Hold it edge on and you'll get a buzz as the leading prong collides. Hold it flat and you don't.

(My dad had a tuning fork. I used to love playing with it.)

- Steve

 

[GBor]

The equation from MikeHalloran's link is basically the same as the one from Greg's original post:

f = k sqrt(E/p), where k = spring constant of a tine, E = modulus of elasticity of the material, and p is the density.

If I'm not mistaken, the sqrt(E/p) is the speed of sound through the material. k would be the resistance to that movement and together, they would make the frequency of a cycle. k should be something like AE/L where A is the cross-sectional area, E is still the modulus, and L is the length of the "beam".

So, Greg, if any of this is anywhere remotely correct, you should be able to input whatever you want and calculate the frequency based on your dimensions and material properties.

As for why the first mode would be symmetric in the "real world", I suspect it has to do with the way the fork is orignially struck. Generally, you strike one tine against something with the other tine of the fork away from the contact point. With that, the "free" tine would accelerate inward while the impact would push the other tine inward as well...180 degrees out of phase.

My 2 cents...OK, that was a littel wordy...maybe it was 4 cents (or it was totally worthless )

Garland E. Borowski, PE
Star Aviation

 

[GregLocock]

Ah, well I think the way the mode is selected is neatly answered by the FEA. The antisymmetric mode involves lateral motion of the handle. So as you hold the handle, you damp that mode out.

Rather more exciting is what happens when you clamp the base. This obviously suppresses the lateral motion of the handle completely, and in fact radically alters the first antisymmetric bending mode, so that by constraining the system we get the usual paradoxical result (for a free free beam in bending) that the frequency drops. That is one of my favourite results from modal analysis. It drops the frequency so much that the antisymmetric mode is below the symmetric mode, which quite reasonably is scarcely affected by the base clamping.

Incidentally I've put all the results into a table on the same page.





Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.