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About Johnmasters

  • Birthday 05/08/1944

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

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  1. I agree with this. It looks like the first or second attempt by a beginner. Even trade fiddles that had different people specializing in certain opperations wouild have better purfling miters.
  2. Do you place the maximum thickness at the narrowest part in the C's ? That would seem consistent with an idea that the back should go from very stiff to quite flexible at the edges. (The narrowest part is intrinsically stiffer and therefore, perhaps putting the maximum stiffness here would be consistent with wanting the largest constrast in stiffness from "center" outward.)
  3. No, Einstein's special theory was accepted almost immediately. Recall that the article was named "On the electrodynamics of moving particle." The Lorentz transformation of Maxwell's equations would not be valid unless the meter sticks were seen to shrink and the clocks run slower. The argument about whether the speed of light was an absolute constant may have been rejected. But it was clear to most that it was not a mechanical wave in an "aether." General relativity was difficult and few (at first) would have understood it well enough to criticise it. Of course, it took 6 years to observe the apparent shift of star positions near the limb of the sun during a total eclipse. Than he was world-famous, overnight. General relativity did not discuss the aether. It took another ten years to finally publish the general theory, and by that time, Einstein was highly regarded, and the special theory was understood and accepted.
  4. There seems to be one question that interests me. For small vibrations, internal stresses will not affect the frequencies of the normal modes. At one time I wondered if arching shape and placement of the inflection line might be placed to mimimize the potential energy in the stresses. The idea was to ask if minimizing stresses in some sense was good for tone. It seemed to me that damping might vary with internal stress in the wood. Also, I expected that a nearly-optimal arch would allow the inflection line to creap over time to minimize any internal stresses. This was a view from noting that the curvature of the surface had positive Gaussian curvature inside the inflection and negative curvature outside. (and zero at the inflection) Would this cause a slow deformation to shift the inflection line slightly? I was curious because of the views of some that arching was more important than graduations. The math would be not of vectors, but of tensors. I came up blind because of math deprivation. Also, I did not see a way that stresses could affect sound except through some kind of damping mechanism. One is nowhere near any kind of buckling forces. I still wonder about the affect of stresses on tone. There is some evidence for it in for example the tightness of a soundpost. But this is not the sort of thing that you are talking about anyway. Or does not seem to be. But there is still an interesting question regarding stresses and sound. I think it is a serious physical question.
  5. Equilibrium is attained when you do not see the violin spontaneously accelerate with no outside forces. (Newton: action=reaction.... do you see?)
  6. This is the same mistake Vigdorchek makes. He considers adjacent areas vibrating while neglecting the fact that they are joined together. (ignoring boundary conditions)
  7. Thanks. The question..... Of course not. That is why I quoted Wolfgang Pauli in the other thread. " It is so messed up it is not even wrong." He is utterly pschizophrenic. He cannot write anything in a letter. He is Swedish, I think, but I do not think it is a language problem. Maybe he DOES have a clear idea. It is just that his idea is bonafide delusion. It is a grandiose scheme and the only thing I can guess is that it is a kind of scaling to make the upper part similar to the lower part. (I read original papers of his several years ago.)
  8. You are likely right about the members of MN are not asking about Lagrangians. I wrote what I did in order to point to Mr. Zuger that the real solutions are nothing he would have guessed. I also realize that other MN people would not guess it either. I was stating what I am sure is the essence of the problem. I see that you must be involved with math or science/engineering and my hat is off. Yes, finite element analysis ivolves solving many equations in many unknowns in a self-consistent converging method. I don't know anything about such an algorithm, but I know that it involves finding a convergence of some sort. In the end, something like a lagrangian approach is at least implicit. So what is your background? I have asked you this before. And I was not talking to the MN folks in my response to Mr. Zuger. I have exchanged letters with him on several occasions and still do not have much of an idea of what he has in mind.
  9. Because a quasi-static model is not proper even though it may appear natural to some. What is needed is a wave equation plus the boundary conditions that relate the motion of different parts of the violin. Such a wave equation will be very detailed and complicated. By boundary conditions, I mean the shapes of all the parts of the violin. The wave equations give time-lags between the motion of one part and the motion of another part. That is one of their principal purposes.
  10. There is a node of sorts. But it depends on the mode of vibration. A given violin has a complete (and orthogonal) set of normal modes. This is true of any such bounded surface. Some will involve portions of the back going along with the top. You can say nothing simple about any of this. It is not simple. It is analogous to quantum mechanics because in both cases one gets eigenfunctions with their eignevalues (frequencies of vibration.) If you cannot understand the nature of these normal modes, you should not talk so "qualitatively" about ANYTHING. As for the rest of you, violin physics is not a mystery, it is just very complicated. Tap tones are the few lower eigenstates of the vibrating instrument. To solve the problem, one needs finite-element-analysis because of the strange and complicated shapes involved in a violin. Numerical analysis, in other words, is the only way to find anything about what is going on. And one more thing, each normal mode will have characteristic damping. There are many kinds and models for damping, and this would make a numerical analysis much more involved.
  11. The Romans used arched forms to support downward loads. Everybody knows that. The differential equations for a curved shell are more complicated than for a flat plate. They are fundamentally of a different sort. For example, curved shells introduce a new variable, stretching of the wood in first order. (Flat plates will have stretching for large displacements, but not to first order.) The new equations involve two more orders of differentiation because of the new variable of stretching. Because you say you are an engineer, I expect that you know about wave equations on different types of surfaces. A curved surface is fundamentally different from a flat one. I expect that Carl Stross will back me up here.
  12. In fact, there is no initial mention of what the central idea of the approach is supposed to be. To paraphrase pysicist Wolgang Pauli, "It is so messed up, it is not even wrong."
  13. The first step is to make an accurate violin. You may never "see through" to things that may make the difference between a good violin and a better one. Your ambition is too grandiose. Simply start by making a violin.
  14. You can put sodium bicarbonate in a frying pan and heat it. It will dance around as CO2 is driven off. When the activity stops, if you taste it, you will find it far more alkyline. It is now just the carbonate. Yes, catnip, I just saw your posting.... sorry for the duplicate
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