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John Masters
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Joined: 13 Mar 2013
Posts: 23
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 Posted: Sat Jan 04, 2014 4:24 am Post subject: |
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If that was for a back in my formula. I like 1.3-1.4 as you indicated for your data point. 1.1 is starting to seem like a weak back, but I do not have data for what was "good" or "bad." I have not made violins for several years as I have had other projects. Also a bit of inertia, hope to get turned around before to much longer.
Averaging the two frequencies seems wrong to me. Let me think it over. At least they should be a weighted average. And then what is the K? It may be OK for comparisons, but perhaps just calculating two separate K's for the two modes might be more meaningful.
I think that I read another paper which could have been later. If this is incorrect, please advise. Or maybe Harris could reply.
Half of mode 2 was considered in combination with mode 5. The net frequency squared was taken to be :
(M5)^2 + (M2/2)^2
This is like pythagoras sum of the squares of two legs. (And the hypotenuse would be the adjusted frequency. This seems more sensible.
Notice that M2 is smaller than M5 and the square is devided by 4. This is the reason that I think that M2 is a small contribution. |
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John Schmidt
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Joined: 11 Dec 2007
Posts: 27
Location: Laurinburg, NC, USA
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| Posted: Fri Jan 10, 2014 4:17 pm Post subject: |
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John,
I am not ready to worry about the Harris formula. I am still trying to either support, or debunk, your formula. I expect to be getting 20 important data points in the next couple of weeks. That should do the trick.
Latest version is found here. http://jpschmidtviolins.com/stiffness_experiment.pdf |
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John Masters
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Joined: 13 Mar 2013
Posts: 23
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| Posted: Sat Jan 11, 2014 6:44 pm Post subject: |
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| John Schmidt wrote: | John,
I am not ready to worry about the Harris formula. I am still trying to either support, or debunk, your formula. I expect to be getting 20 important data points in the next couple of weeks. That should do the trick.
Latest version is found here. http://jpschmidtviolins.com/stiffness_experiment.pdf |
Hi John,
Consider that different strings are made a certain mass per length and are designed for given tensions. Over the entire range of strings, there is a limit to mass and "stiffness" (which means the tension, not the ability to bend the string.)
The string goes one way, and the bridge and body move in response. If you drive a SHO at resonance, the motion will be 90 degrees out of phase with the driving force. The amplitude of motion will be infinite with no damping. With damping, there will be a limit to motion. The SHO article in Wiki ought to show show limits of motion vs driving frequency. The more damping, the lower the response and the more the graph spreads out in frequency. This set of graphs often is used to discuss the Q of the resonance.
If a violin is very stiff, it might do better with heavier strings at more tension. There must be a relationship that keeps all strings withing certain limits of size and tension. I think this would roughly correspond to the limits within what stiffnesses and masses ought to be in the parts of a violin.
I hope you find some exceptions, I really do. It would be interesting. You won't be debunking anything as I have not claimed any virtues in the formula idea, And I never looked for a relationship between the effective stiffnesses of top and back. If you have a range of stiff and weak violins, see if the lighter strings tend to work better on the weaker (structurally) violins. This might be interesting and would tend tell you something.
In your paper, the plate is not a harmonic oscillator, but each Mode is considered to be analogous to a SHO. That assumes that modes do not overlap and there is no driving of the resonance. Free motion. |
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