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Hmmm... great! So an equation requires something. I alway thought it should serve to calculate something. Certainly, calculating vibrations of an anisotropic plate is much more complicated than doing it for an isotropic plate...

I don't believe what I don't understand.

Here's another novelty, brought to us by Jack Johnston:
Source: http://jackjohnstonguitarmaker.com/aboutus.aspx

Good to finally know what Stradivari really did!

Of course, I do not doubt that Jack Johntson's guitars sound better (have not heard them, it's just a matter of trusting him). But also be aware of his disclaimer:
Source: http://jackjohnstonguitarmaker.com/TheT ... terns.aspx

Oh well...

* * *

But rants aside and back to Luigi's (your) "problem" or task:

As far as I understood you want to do (or you want Luigi to do) a research about the usefulness of Chladni pattern testing (records) in guitar making. Chladni patterns are just one way to look at the vibrational behavior of an instrument (or parts of it). There are more ways to do similar but not identical analysis, like for example looking at spectrograms, or measuring sound pressure levels inside the guitar, and more. I am afraid that a full understanding of the meaning of the Chladni patterns implies reading much more than just about them, due to the fact that most (maybe all) serious publications after Chladni don't treat this phenomena (of the patterns) as a "standalone discipline". You (Luigi) will have to go there and read a lot about acoustics to get relatively few pieces of Chladni pattern related stuff. But it's exactly this relation which makes the whole thing interesting and useful.
I'm not sure if you know this: http://www.speech.kth.se/music/acviguit4/
If it's new to you just browse first through it, heading for vibration modes (which is not really the big part of it, but they are given some importance there, and in the end you will have gone through all of it anyway and you will have another piece of the mosaic! )

Another possible line of inquiry is human perception of guitar acoustics. E.g., double-blind listening tests of ~small changes in guitar construction, component selection, playing technique, etc. With the plethora of subjective opinions about the effect of this or that bridge material, finish gloss level, bridge pin material, etc, etc... a controlled study could do a lot of good. Millions of variables to choose from, of course, so Luigi could pick whatever is of interest to him. These can also be tied back to spectral analysis and/or other acoustic techniques. Variables that can be analyzed by modifying 1 guitar are a lot easier to study; else you need many otherwise identical guitars for the stats to work -- but it need not be a reversible modification if sounds are recorded and played back.

The math/physics/engineering requirements drop a lot (though some stats like t-tests would probably be needed), while psychology goes up. The scientific method is even more important in these kind of studies because of bias potentials. A double-blind approach poses some practical challenges, but there are plucking devices to take the player out of it, and recorded sounds can be presented randomly by a computer. ABX testing is a good place to start for null hypotheses--lots of examples from the audiophile community on it.

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David Malicky

If he's interested in working with Chladni patterns, one thing that's useful in gaining an understanding of what you'll see on a guitar top is to start with square isotropic plates. The easiest ones to use for that are expanded styrene beadboard, which you can get at any lumber yard. You can cut various shapes and see what happens to the modes. You can also cut rectangles of wood and try to relate the mode patterns to things like Young's modulus in the different directions.

I've been wroking with Chladni paterns for a long time. They're not 'magic'; there is no magic in this business. There does seem to be a relationship between what the Chladni patterns look like and the sound of the assembled guitar, but it's nowhere near as simple as saying 'closed Ring= great sound'. The pattern shapes do tell you something about the distribution of mass and stiffness within the plate, and there is probably a relationship between that and the tone, such that duplicating the patterns should be a way to get close to duplicating the tone. But there's a lot to this, and a great deal we don't understand as yet.

I do think of the frequencies of the 'free' plate paterns as being a _very rough_ indicator of the stiffness to weight ratio of the top. Assuming the weight is about 'right' then the stiffness will be too if the frequencies are 'right'. Again, not as neat as you might like, but useful in some degree.

Of course, there is no simple way to predict the frequencies of the assembled modes from the 'free' plate Chladni patterns. There must be a relationship, but with all the other variables that Trevor mentions, it can't be anything simple. Then there is the issue of what the frequencies of the assembled modes 'mean'...

There's no need for strain gauges to measure Young's modulus. There's the static "beam deflection method" where you load the beam, measure it's deflection and compute the Young's modulus using the standard beam deflection equation. Or, if you are doing a lot of wood, there's the dynamic method, where you tap the wood, measure it's frequency of vibration and stick those numbers (and a few others, like those you need to compute density) into an equation and it gives you Young's modulus (and density). If there's a lot of wood to do, the dynamic method is way quicker. I've cross correlated results from both methods and the answers come out the same to ~1%.

Either way, much of the work is in the sample preparation. In both cases you need uniform thickness and smooth surfaces, preferably planed. Planed wood measures up as stiffer because the surface fibres of the wood take a lot of the load. These fibres are "mashed" on a sanded surface so add to thickness and mass but not to stiffness and strength. A hand planed surface, on the other hand, has the surface fibres intact. The dynamic test needs panels to be rectangular, too. All of this work has to be done, anyway, if building with the wood, but is quite a lot of work if you're doing a shop full of wood in one hit. (But isn't that what the "apprentice" is for?)

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Filoppo Morelli wrote:
"From an experimentation perspective though, Luigi got interested in your assertion early in the video about density in relationship to Youngs Modulus. So he's working on a hypothesis whereby he intends to go through all the top inventory we have and vet out the observation that YM is significantly related to density."

Please be aware that it's only the E (YM) values for deflection _along_ the grain that correlate with density, and then only for _softwoods_, which all have more or less the same structure. 'Compression grain', present in wood near the bottom of large trees, which is characterized by relatively heavy latewood lines, tends to be denser in relation to it's stiffness than most, and wood from high up in the tree may be a bit lighter than the stiffness would predict.

The only thing that correlates at all with cross grain stiffness, as far as I can tell, is how well quartered the wood is.

I would think that so long as your surface treatment and thickness are consistent, then your measurements would be, even if they were not 'correct'. In other words; if you sand all the samples to, say, 3.0mm thick, with the same grit of paper, you'd rank all of them in the correct order for stiffness and density. If you re-did the measurements with the same samples, but now hand planed with a sharp cutter to 2.5mm thick, you'd get somewhat higher E values, and somewhat lower density. The planed values would be closer to the 'truth' for those samples, but no measurement is perfect.

The question then is, what are you making these measurements for? If all you want to do is decide which tops are 'better' in terms of mechanical properties, than all you need is an accurate ranking, and the sanded values should be fine. If you're using the numbers to figure out the absolute limit of thickness that will be just stiff enough to work, the planed values would be better, but not necessarily 'right'. Even then, any good maker would leave a safety factor; make the top a little thicker then the absolute minimum, if only to allow for final sanding. If you're trying to figure out something about the relationship between wood structure and stiffness, and want to develop equations to relate different parameters, you might need to be much more accurate than any home-brew test.

I'll note, too, that these tests are only really accurate if the width and thickness of the pieces being measured are 'small' relative to the length: to get accurate results you need to test long, narrow, thin strips (which can't be made into tops!). 'Poisson's ratio' couples bending along and across the grain, and has to be negligable for the properties not to effect each other. As the long-grain and cross-grain resonant pitches get closer to each other the 'Poisson coupling' changes the straight lines of long-grain and cross-grain bending into 'ring' and 'X' modes (and alters their frequencies and damping, too!) Such strips are not going to be representative of the whole top they come off of: again, you know what _that_ strip does, but maybe the one next to it is different? Once more; no 'perfect' test.

Basically, as per Al. If you want to compare your results to others, I'd go the planed samples. You might get a little less dispersion in the measurements also. If you just want to rank stuff, no problem, just treat them all the same.

The aspect ratio of the samples is an issue as Al pointed out, but it only really becomes problematic when the aspect ratio of the panel approaches the ratio of the long and cross YM to the power of 0.25. When this happens, the node lines of the first bar mode of vibration get seriously curved. If the lines are straight, you tend not to have a problem and the dynamic method of testing still seems to give good results. Chladni testing will indicate whether or not you have a problem, as you will see the curved node lines, indicating coupling between the long and cross modes of vibration.

If wood testing is of interest, there's probably some stuff on Brian Burn's site, (Lessonsinlutherie) and there is also this paper, if you haven't already downloaded it (I've mentioned it a few times, so apologies to those who are tired of seeing it!)
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PMARCW000012000001035001000001&idtype=cvips&prog=normal (Also downloadable from my site under "about" / "technical"). It deals primarily in the results and insights from testing rather than the testing procedures per se.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Sanded is fine as long as all your samples are either:
- approx the same thickness
- different thicknesses, but all so much thicker than the layer of mashed wood that it is insignificant in the h^3 term.
But, it doesn't work to compare a relatively thin sample with a thick sample: the mashed layer is a substantial % of the thin one, so h^3 will be inflated more than for the thick one.

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David Malicky

One issue with testing panels, such as guitar top halves, is that there can be a lot of other modes besides simple bending ones that can sneak into the same frequency range as the bending modes you're looking for, and cause problems. For example, there's a bending/twisting mode, with two lines across the plate and one up the center along the grain, that can come in somwhere near the crosswise bending mode pitch. This one involves the lengthwise Young's modulus, and a combined shear modulus. When this happens the crosswise mode can look more like a fish: with a rounded 'head' at one end, a pinched in area, and a 'fish tail' at the other end of the plate. Sometimes you'll get two 'fish' modes, facing opposite directions, at different pitches, and not see a 'real' crosswise bending mode at all.

Any time you see 'mixed' modes like that, the frequency and damping data is also mixed. A good example of that is the 'X' and 'O' mode you see on a square isotropic plate. This happens because the 'lengthwise' and 'crosswise' bending modes are at the same frequeucy, and the Poisson ratio kicks in strongly, so that they add up in- and out-of-phase with each other at different pitches. Ideally, the _average_ of the two frequencies is the 'real' lenthwise/crosswise bending frequency, and the _difference_ between them is a measure of the strength of the Poisson ratio of the material. In this simple case, then, you can use the 'distorted' coupled modes to figure out what the 'ideal' mode frequencies would be, and determine some of the material properties. This only works when the 'X' and 'O' modes are perfectly closed, which is sometimes hard to determine. Sadly, it probably doesn't work in cases like that 'fish' mode, because there's more going on than simple bending.

As Trevor says, you use the curvature of the node lines to tell you when another mode is 'too close for comfort'. In these cases, if you really need to know the properties fairly exactly, you will have to change the aspect ratio of the plate to shift the relationships. This can be difficult if you're planning on making a guitar out of the wood later.

Of course, there's _always_ more going on than simple bending (*sigh*). According to one article on wood properties I've seen, by McIntyre and Woodhouse, determining lengthwise and crosswise Young's modulus via the bending mode frequencies only gets you within about 10% of the 'real' values, even in the best of circumstances, because of the perturbations introduced by the other modes. To get closer you need stronger mathematical tools, data on the other modes, and probably a computer.

It occurs to me as I type that the _real_ science project here might just be one on the limitations of measurements, and how you can use various methods to cross-check things and reveal biases to get you closer to that unattainable 'truth'. This would be a great thing for any young scientist to internalize early on.

Ain't that the truth!

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

David Hurd has a good book on the science and engineering of guitars http://www.ukuleles.com/LBLBook/TOC.html He includes equations and a whole host of various spread sheets for performing calculations using the data you collect. Many spreadsheets are also on his web site as well as other related info. He also includes some directions for shop made data collection devices.

When asked at GAL "what is the most useful to put to work now for making guitars", Al C. pointed me to Mark Blanchard. http://blanchardguitars.com/guitarpages ... ladni.html

Good luck.

Ed

On the sanded versus planed situation, when I set up my spreadsheet for working out youngs modulus from defection testing, I deducted a few thousandths of an inch for surface condition,

Hi Trevor, I was wondering what the equation for the dynamic method is

E=[0.94*(Density)*(length)^4*(frequency)^2]/[(Thickness)^2]

("marimba bar" vibration mode)

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au