Edge Thickness and Mode Frequencies

[Shunyata]

Has anyone looked at how edge thickness affects free plate mode frequencies? 

Seems like thicker edges would increase free plate frequency, but this impact would largely disappear once the plates were attached. (The ribs REALLY stiffen the plate edges!) Similarly purfling  choices might impact edge stiffness and frequencies.

[Cathode Ray]

Don't hear much talk about this(area) but I would think edge compliance would be a significant factor. Channel depth, placement and purfling groove depth all being contributing factors. Perhaps even lining size and material.

[scordatura]

This is a good question. I have a feeling that many makers don't consider this as a variable because they have their approach that does not change unless dictated by the model. Intuitively, I would think that even when the plates are glued to the rib garland there would be a small effect. Some makers don't even finish the edges until after the plates are glued to the ribs. 

[Don Noon]

With free plate taptones, the edges of the plate flap a lot... so it's hard to say if the higher stiffness of thicker edges will make the taptones go up, or the added mass will make the frequencies go down.  Maybe Marty has something in his files about this.

But the edges of the plates don't flap like that when the instrument is assembled, so while I DO record free plate taptones, I continue to consider them mostly as a distraction from what matters.

[uncle duke]

One way to see would be to have 4.4 mm edges after purfling is installed, do all of the scraper work to make the plate look good, take note of the free plate tap tone and then lower the plate edges to, for example, 3.3 mm, gouge the purfling area again and note the change. 

 

[Anders Buen]

In general the edge thickness correlates with the average thickness of violin plates. However, the edges tend to become thinner by wear and one can of course choose to keep them thick or thin at will. I do not have much experience in doing edge work on assembled bodies. But I understand that this may give changes to the body modes.

I guess George Stoppani is an expert on this and his pinning of the plates before assembly may give a situation somewhat similar to the assembled violin. I think he has said that the central tinning does most. The talks VSA have run are on Youtube. One of these are with George. 

[Marty Kasprzyk]

8 hours ago, Anders Buen said:

In general the edge thickness correlates with the average thickness of violin plates. However, the edges tend to become thinner by wear and one can of course choose to keep them thick or thin at will. I do not have much experience in doing edge work on assembled bodies. But I understand that this may give changes to the body modes.

I guess George Stoppani is an expert on this and his pinning of the plates before assembly may give a situation somewhat similar to the assembled violin. I think he has said that the central tinning does most. The talks VSA have run are on Youtube. One of these are with George. 

His talk is on 

I listen to it then and a few times I've replayed it.

[Marty Kasprzyk]

In general when you thin a free plate in areas outside of the node lines of a mode the frequency (f) will go up.  The reason for this is that those areas aren't bending much so they don't contribute much to the mode's stiffness (S) but they do add mass (M).  So reducing the thickness reduces the weight more than it reduces stiffness so this raises the frequency of the mode from  f = (S/M)^0.5

If you thin the free plate in areas inside the node lines the mode frequency will go down. The stiffness is proportional to plate thickness cubed whereas the mass is simply proportional to thickness so thinning decreases the mode's stiffness more than the mass so the the mode frequency goes down.

The attached photo shows the mode 2 and mode 5 shapes of one of Joseph Curtin's top plates from his 2006 VSA Papers article "Tap Tones and Weights of Old Italian Violin Tops".

So by choosing where you thin you can adjust the mode's frequency up or down.  If you are a plate tuning nut you can carefully alternate the thinning certain areas so the frequency doesn't change at all as you thin the plate.  This gives the impression that you are using a high radiation ratio (RR)wood that has a high speed of sound (c) to density (p) ratio  (RR=c/p) because a high mode frequency can be achieved with a low weight plate.  Thus leading to belief that the Old Italian makers used specially good wood.

While you are at it you can adjust the mode 5 to mode 2 frequencies by choosing where to thin the plates.  For example if you thin the plate edge between the mode 2 node lines the mode 2 frequency will go down while the mode 5 frequency will go up therefore giving a higher M5/M2 ratio.  The attached photo of a top plate of a Strad 1714 shows the areas around the upper and lower blocks are thinned whereas the Curtin plates are left thick (Sacconi platform).  Thus the M5/M2 ratio of the Strad top plate might be higher than the Curtin plate.

Mode 5 is also proportional to the longitudinal elastic modulus of the wood while the Mode 2 is proportional to the cross grain elastic modulus of the wood.  Therefore it is sometimes perhaps mistakenly assumed that Old Italian top plates had a high M5/M2 ratio (about 2.3) because of the special wood they were using rather than to how they thinned their plates. 

 

All of the above refers to free plates.  But when you completely clamp the plate edges everything is reversed.  Most of the plate bending now happens at the plate edges.  So thinning the edges will probably reduce mode frequencies.  Thinning the center areas will probably increase the mode frequencies.

But the assembled violin's plates glued to the ribs have something between a free plate condition and a fully clamped edge condition.  The plate is able to move sideways because the thin ribs bend but it can't move much vertically and the plate edge can now also rotate.  

George Stoppani's new method of temporarily holding the plate at its edge with an array of fingers comes much closer to duplicating a real violin's glued plate condition.  The plate thinning effects on mode frequencies are likely to correspond much better to the glued together assembled violin's modes than free plate tuning.

 

I'll try attaching a top plate with Velcro and skip the gluing.

 

[Peter K-G]

Marty,

You have knowledge in free plate modes!

(so do I)

The point is not what edge thickness does, but how different density materials has to be for the assembled violin to turn out.

It's not complicated, it's knowledge!

(BTW rocket science is not complicated, ask Mr. Musk)

[Marty Kasprzyk]

On 1/13/2022 at 10:35 AM, scordatura said:

This is a good question. I have a feeling that many makers don't consider this as a variable because they have their approach that does not change unless dictated by the model. Intuitively, I would think that even when the plates are glued to the rib garland there would be a small effect. Some makers don't even finish the edges until after the plates are glued to the ribs. 

I think it is a good question too.  Sacconi, in his book "The Secrets of Stradivari" suggested that Strad glued his plates to the rib assembly and then shaped the outer shape, cut the purpling groove and installed the purfling, and then scraped down the plate to its final edge scoop and shape.

It is my pure speculation that he might have first strung up the violin to see how it sounded and he then scraped the outside surface of the plate and the edge scoop region down to adjust the sound. 

A maker today could use the same sequence to see how the sound changed as the edge shape is established.

Or on the other hand maybe he didn't much care and he just make everything look nice and once in while they sounded good too.