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the function of arching shape


reguz

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20 hours ago, reguz said:

 Without those curves (that is, with a flat top and back) your instrument wouldn't be able to stand up to the pressure of the strings.

The arch doesn’t help the back to stand up to string pressure, and the top is supported by a bass bar and sound post. In addition the arch doesn’t extend from one side to the other or one end to the other but it ends at the channel. So it isn’t that the ribs are carrying the load of the strings in the way the pillars support the load of an arched bridge. If anything the channel (of the top) supports the load and it is arched backwards. 

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On 9/10/2023 at 6:16 PM, Anders Buen said:

The arch is likely to come from empirical means. Some stringed musical instruments are made of natural cavities from seed containers, or the like. Some are simply hollowed out. 
By the answers here I can see that you are likely to have the "answers to all this" yourself, and do not pay attention to what I have written.

Moderately curved plates work better because they can be made thinner and the design, if it is of the right type, will resist and survive humidity cycling better than the less good designs, like too high arch and too fast changes of the curves.

Arch suppress the low frequency response and does little to the highs. Maybe a balance there is achieved in better instruments. It is perfectly possible to make a useless instrument with "right arch", but other important factors incorrect. Arching itself does not make the sound. Violin sound and instrument stability is a balancing act of lots of factors.

Dear Anders read my report

Maestro 2023 in september.docx

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On 9/11/2023 at 2:04 AM, FiddleMkr said:

So it isn’t that the ribs are carrying the load of the strings in the way the pillars support the load of an arched bridge.

Actually, they are.  A top supported by ribs, with or w/o a channel, can support a string load, and in addition the force density vector at any points along the ribs may be identical for two plates, one with and one without a channel.  Put the string load on any plate that lacks rib support and the center of mass of the plate will accelerate according to force = mass * acceleration whether there's a channel or not (edit - this may be an incorrect example since the string load is not an external force).  I mean, of course discrete supports and a continuous support aren't identical, but that's not what we're talking about is it?  This doesn't mean reguz is correct.

Nope - I agree your point is supportable.  Bridge pillars primarily support a vertical gravitational load and some bending moments, primarily at the bridge ends depending.  Ribs don't support a vertical gravitational load.

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4 minutes ago, Dr. Mark said:

Actually, they are.  A top supported by ribs, with or w/o a channel, can support a string load, and in addition the force density vector at any points along the ribs may be identical for two plates, one with and one without a channel.  Put the string load on any plate that lacks rib support and the center of mass of the plate will accelerate according to force = mass * acceleration whether there's a channel or not.  I mean, of course discrete supports and a continuous support aren't identical, but that's not what we're talking about is it?

What support the rib structure for the load condition from the top? That is what you must explain!

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1 hour ago, reguz said:

What support the rib structure for the load condition from the top? That is what you must explain!

Not really.  I don't mean to be disingenuous but I was replying to FiddleMkr's assertion.  Regardless I should amend my above response since there's another way of looking at things. 

The string load is internal to the violin, so in the absence of gravity the center-of-mass motion of a free-floating object would be stationary, i.e. the sum of the forces in any direction are zero.  This is going to be tough w/o drawing diagrams and I want to keep it simple (even though it isn't, even in the static case)...without a back or ribs the string tension would create downward force (say pressure*bridge foot area) born entirely by the top plate that is compensated by the sum of the upward average forces at the string attachment points, say the tailgut tension and at the pegs, which don't exist yet.  There's also rotational moment about the cm: on the one side is the average vertical peg force times the average distance from the cm to the pegs, and on the other (I assume the cm is on the pegs side of the bridge) the vertical forces at the bridge and the tailgut tension times their respective moment arms.  The sum of these are also zero.   There are also equal and opposite horizontal compressive forces from string tension countered by reactive plate compressive stress.  Gad, I may regret this - I'm getting like reguz...

Adding ribs would seem to primarily increase the area integrated over to obtain the average forces and moments in the principle directions, reducing the amount of rotation-induced deformation of the top plate required to reach equilibrium and the horizontal reactive stress in the top plate.  Adding the back seems to act similarly, maybe primarily countering rotation - until the soundpost is added.  This both adds an additional rotational moment on the tailpiece side of the bridge (hmmm - does it?...yes I suppose, but there's an equal and opposite moment at the bottom plate.  That seems right...) and adds a vertical reaction force, which reduces the average vertical reactive force of the top plate alone to the strings since the sum remains zero.

So what does arching do?  At least it determines how the forces acting on the plate are distributed through the plate, but this comment has gone on more than long enough.  I just want to get a feel for a free-floating violin.

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2 hours ago, Torbjörn Zethelius said:

Andreas, have you done this? It seems a useful experiment.

Torbjörn, ultra thin ribs were the starting point of my super light violin. I used 0.2 mm thick maple which I reinforced with Japan paper. Plates of top and back were absolutely normal, maybe even a bit on the heavy side.

The result was the complete collapse of sound. So this means simply that the rib structure determines what you can do with top and back. 

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1 hour ago, Dr. Mark said:

Not really.  I don't mean to be disingenuous but I was replying to FiddleMkr's assertion.

Thank you Dr. Mark. Do you understand what I have written and agree. If not just let me know on what.

What w can think of is having a building with 2 or three floors. The upper load down on the floor bellow and so the next untill the structure reach the soil Mother earth. That is a stable "structure" If there is no soil the buildeing fly away uncontrolled. That we must compare with the load on the top-- on the rib--on  tha back and ---- nothing structure.

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1 hour ago, Andreas Preuss said:

Torbjörn, ultra thin ribs were the starting point of my super light violin. I used 0.2 mm thick maple which I reinforced with Japan paper. Plates of top and back were absolutely normal, maybe even a bit on the heavy side.

The result was the complete collapse of sound. So this means simply that the rib structure determines what you can do with top and back. 

The ribs should match the plates for a fair balance. Just my intuition telling me this, no research.

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38 minutes ago, David Burgess said:

I think it was Colin Gaugh's research which showed that the stiffness of the rib assembly makes large differences in the way the plates vibrate, and the way the instrument sounds.

Colin varied the rib stiffness over a factor of 1,000,000, so it is not very surprising that it shows a large difference in mode freqiencies.  Rib stiffness of normal construction would be within a factor of 2, and the effect on vibration would be a lot less.  If you make ribs .2mm thick, that would be different... but not by a factor of a million.

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4 hours ago, Dr. Mark said:

Actually, they are.  A top supported by ribs, with or w/o a channel, can support a string load, and in addition the force density vector at any points along the ribs may be identical for two plates, one with and one without a channel.  Put the string load on any plate that lacks rib support and the center of mass of the plate will accelerate according to force = mass * acceleration whether there's a channel or not (edit - this may be an incorrect example since the string load is not an external force).  I mean, of course discrete supports and a continuous support aren't identical, but that's not what we're talking about is it?  This doesn't mean reguz is correct.

Nope - I agree your point is supportable.  Bridge pillars primarily support a vertical gravitational load and some bending moments, primarily at the bridge ends depending.  Ribs don't support a vertical gravitational load.

My sentence you commented on is taken out of context, and doesn’t reflect what I meant. I was trying to compare an arched bridge with pillars at each end, to a violin back (or top) supported by the ribs at each end. The plates may resemble an arched bridge, but they can’t function that way, for several reasons. The back is loaded upside down (with the sound post) so it doesn’t function like an arched bridge. The top has a base bar and sound post lengthwise that is unlike an arched bridge. So you are left with the top’s sideways arch that resembles a bridge and it’s loading. But even in this case the arching ends at the channel before the plate lands on the rib.  
      So the ribs do support the load (of the strings) on the the top-much like the pillars of a bridge- but the top nor the back functions like an arched bridge, which is what I meant.

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27 minutes ago, Andreas Preuss said:

You can put it like this. However, I think the ‘acoustic impact‘ of rib construction is one of the most neglected aspects in violin making.

You may be correct about that. I see the rib structure as a means to create space inside the acoustic box for the air to move. I wonder what more you could do with that.

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4 hours ago, reguz said:

What w can think of is having a building with 2 or three floors. The upper load down on the floor bellow and so the next untill the structure reach the soil Mother earth. That is a stable "structure" If there is no soil the buildeing fly away uncontrolled. That we must compare with the load on the top-- on the rib--on  tha back and ---- nothing structure.

To be clear, gravity and the normal force of the soil are external forces relative to your building.  If we take away the soil and leave gravity then the center of mass of the building will accelerate, but if we take away gravity and leave the soil then the building will just sit there.  The soil provides an equal and opposite, but reactive, force to gravity.  I suppose we could treat the bridge feet, the pegs, and the tailgut and endpin as points where an external force is applied to the violin, something like the string on an archery bow - with a hand and an arm and etc. etc. as well) but I don't think I'd do that.  You may wonder why not?  I'd probably answer that it's because I'd have to ask why the center of mass of the violin body isn't moving considering that there's a net external force on the violin, and I don't like to do that if you know what I mean.

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On 9/10/2023 at 5:38 AM, Anders Buen said:

The main function of the arching is the stability it provides the instrument for its rather thin plates. Moreover, the arching makes it possible for the bowed instruments to go through humidity cycles through the year and with travelling A to B in climate C, like a dry airplane cabin.

The tonal aspects of the arcing is a secondary effect. But it is probably there.

As to the Original Post, there are many discussions to have about the statement/ question.

But like tap tones, the isolated data is not as helpful, thought there are many who achieved solutions.

The complexities in all this is the entire system.

But having shopped the past two years ( 2022/ 23 ) about this time ( end of summer/ fall ) for relatively inexpensive instruments that are better instruments, ones that are responsive both small and large, reasonably loud and pleasant for the player, there are archings and patterns that are preferred. Locating any known DGD pattern at the lower price point is difficult, but the Strad is a known.

Maestro Buen's reply is a very valid starting point for an exhausting discussion.

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2 hours ago, David Burgess said:

Yes, but it wasn't done in 1,000,000 increments, was it?

I couldn't find in the paper how many increments were calculated to make the plots.  It's all Finite Element Models, so he could have done however many increments he liked.

Only ONE aspect was varied:  the strength of the ribs.  If you also looked into varying the wood properties, plate weights, and arching, I think you would end up with a solid blotch rather than lines, which would be of little use in predicting body mode frequencies from the plate modes.

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1 hour ago, Don Noon said:

Only ONE aspect was varied:  the strength of the ribs.  If you also looked into varying the wood properties, plate weights, and arching, I think you would end up with a solid blotch rather than lines, which would be of little use in predicting body mode frequencies from the plate modes.

I like experiments which involve only a single variable, when that is possible. You don't?

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I see the violin under string tension as a bit like an archery bow. The big difference is that an archery bow has its greatest mass and stiffness at its centre with most bending confined to the limb ends. But a violin with its weakest part at its centre bout might have a tendency to buckle in that area. So I think a violin made strongly enough at the centre bout might be more responsive than one weak in that area.

I don't see the top or back arching being all that important in that respect.

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