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About Johnmasters

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  • Birthday 05/08/1944

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    Physics of violins
    Finite element analysis for eigenmodes, stresses, whatnot

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  1. An FEA program which considers the top a simple shell with no extra thickness at the end blocks shows a definite depression at the two ends. I use all cross-directions for my curtate cycloids, as you seem to indicate that you do according to your templates. I programed my machine to program all curtate cycloides, and this does not have a recurve at either end. It is a very gradual change, so it does not look "fat." The results have seemed to work well. I still of course leave the extra wood for the block gluing, but this not a physical constraint on anything importantn IMHO. If you wish to replay, do so. Most people do not reply to my remarks, but I make them anyway. I have also done considerable study of stress-strain deformaions on decent models of plates. I use many more points than you see in the simplistic models from Schlescie. I have done both single shells and thin plates as I have 1000 nodes abailable. A plate takes about 380 points per surface. (I use the student version of ABAQUS) And most people have not done such calculations. Most use CNC with models drawn in other ways, not the way I have done. (My longitudinal arch is not a curtate cycloid.. I devised another curve which is analytic and it can be adjusted as to shape analytically.)
  2. Yes this is a great invention from the automotive field. Shim under valve stem.
  3. Perhaps damp wood is more flabby, and the stiffnesses involved have decreased. Keep in mind that a resonant frequency of a mode is of the form of square root of (k/m) where k is some kind of stiffness, and m is an effective mass involved with the resonance. (I don't mean resonance of the entire violin, I am thinking of the resonance of a particular mode.) Mode frequencies and move downward with decreasing stiffness, and perhaps even more important, damping could increase. Damping is a difficult property to measure and there are many ways to model it. You might compare a bassbar blank dry with one soaked in water.. That would certainly suggest something to you.
  4. Perhaps there is more than one protein; one hardens (makes bubbles) upon exposure to air, whereas the other does not. I know that heat changes at least one protein. Oh, I see that Mampara has already pointed out such a thing.
  5. You need to also consider the reflections of the wave from the boundary. Intuition is useless unless you actually can solve the problem. At least, I can see that there are two distinct resonators here; a somewhat simlar situation is involved with those Carribean drums with the hollows beat into them. I suspect a good model and proper solution would be quite difficult. Don't even try to think of an explanation.
  6. Ha Ha !! That is a new piece of information for me. Most of my violas were sold to advancing students, and I never had complaints. So this is new to me... I would explain how certain things were compromises, such as broader bodies for a given length. I tried to keep the string length down a bit from standard sizes by enlarging the lower bouts a very small amount. It seemed to give good results.
  7. Well, don't forget that violnists are notoriously neurotic. Violists, not so much. Do you make such adjustments for local densities in the wood? Does that help, or is that just a loose concept?" I don't think that I have ever seen a top or back that varies significantly in density over the size of a violin or viola; at least decent wood seems pretty uniform. If it was NOT uniform, I would not see good justification for leaving it slightly thicker in a small area. As I said before, an effective stiffess for mode 5 gives a good adjustment for a given piece of wood. There is another measurment that I believe corresponds to Don's radiation ratio in a near-finished plate. That would be the frequency of mode 5 divided by the mass. For a spruce top, I invariably get a superior result if this is 5 or more. Much below 5, and the sound is less alive and perhaps a bit muted.
  8. Don, can you think of any mathematical approach to calculate the maximal rigidity of a top plate while holding the height of the arching constant and of course specifying the edge boundary conditions ? I mean, for a given (perhaps constant thickness) calculate the arching which gives a maximal compression stiffness. I am sure there is a solution, but it might involve theorems in non-flat geometries.
  9. But if everybody knows everything, how will that affect the markets if there are a couple hundred makers all chasing customers with $15,000 violins
  10. David, do you have access to sets of wood that come from the same trees? And how closely can you duplicate archings and graduations? Do you find an "effective stiffness" of plates? I got some resistance to this idea in previous posts. My only intention was to relate two measurable things. I have found that a certain relationship that gives my 'effective stiffness' is at least a way to reject plates that do not seem to give a decent outcome. My only criterion for a good outcome is an open sound with good strength. I let timbre be considered as something that will result from much playing. Of course, the physics is complicated, but it is not unknown physics. Nobody seems to have taken the time and expense to correlate the many properties of modes and the higher 'forest of modes' including the bridge hill using finite-element analysis with damping. This is hard to do; there are many models for damping, and such an investigation would take a lot of time and an FEA program something like Boeing Aircraft may own. That means millions of dollars, I am sure.
  11. Each MODE of the violin can be seen as approximately a simple harmonic oscillator with an EFFECTIVE stifness. Besides, with two pieces of data, mass and frequency, what would YOU do? This is better than doing nothing, and I have found good correlations. For example, if I cannot get an effective stiffness I like with my thicknessing, I have found that it is better to start with new top wood. I have found this an improvement in many cases. So it is not "physics about a violin," it is physics of a single mode of a resonant body.
  12. In other words, just choosing light wood is not necessarily a good idea. The idea is to choose wood that gives a particular relationship between mass density and intrinsic stiffness. (The bulk modulae of the wood.) I have in the past chosen light wood that was also either too weak (soft Englemann) or too stiff (Sitka) and found that I did not like either one. I prefer the Picea Excelcius which is usually sold by the German wood companies.
  13. Assuming that you have already chosen the wood, I have found (and Harris later found a modified version) one test for the effective stiffness of a plate. This is modeled on the simple harmonic oscilator and involves mode 5 in my treatment. Harris later added a consideration of mode 2. I took the frequency of mode 5 squared times the mass. The square root of this gives a quantity which has units of a stiffness. Harris took the square of the frequency of mode five plus the square of mode-2 frequency and added them. The contribution of mode 2 in that case is a small change as mode 5 dominates. This may be useful if you want to have some sense of the properties of the wood of the back and top and how to adjust graduations for them. I have found that it is a little better than considering tap tones alone (without using the mass.) People have asked how to use the mass measurements along with tap tones, and I have found good predictions by combining them in this way. After that, one must have "good" wood. Damping of various modes or modes in certain ranges of the spectrum would be important. It is difficult to know how to choose the proper wood with that in mind. Perhaps it is totally empirical and one just needs to know how to select wood. As I said, the above assumes you have a given set of wood and want to optimize it. You can keep track of various measurements and compare wtih your outcome. The method is particularly useful to adjust the average thickness of tops. For the back, one still has the freedom to bias thicknesses toward the center or make them more like the classic textbook instructions. I have seen the cat-scan photos of various backs, and it seems that many good violins have extra wood in the center, and various approaches to the question of how much extra thickness should extend to the position of the soundpost. If this last idea has use, it could have been implemented by older makers by making the entire back a bit thick and then voicing the white violin by scraping areas of the back. A nearly-finished back is easy to scrape smoothly without destroying the surface. If this was done, it might correspond to the trimming of bridge holes that most people do. In any case, it is not silly, and it is not a crackpot idea. The physics is easy to show, and people with no exposure to physics should not be so skeptical and dismissive.