Hello Richard, A few comments interspersed below. Richard Brekne wrote: > I re-read this and think we need to back up a bit here. > > Throwing sand on the soundboard and just smacking the bridge with a > hammer is not really how the process of displaying Chladni pattens is > accomplished to begin with. One uses a modal hammer to excite the panel > and read the results with a series of accelerometers so as to ascertain > the soundboards reasonant frequencies. But one doesnt create Chladni > patterns this way. > > Chaladni patterns are created by exciting the panel to one of the > reasonant frequencies found, and you dont do that by just taking out a > plastic hammer and smacking the bridge with your hand. The lowest > reasonant frequency is usually around 50 hz or above and you are going > to have a good time hitting the panel with a hammer 50 times a second. > I think the distinctions between conditions arising from free and forced vibration should be drawn and given their due in the question of the sand thrown on the board and resulting figures. Chladni figures can be produced on the soundboard by tapping it even though not at the resonant frequency for its free vibration. This happens, as the reflected and superimposing strain wave in the board divides it into distorting and dilating areas, as you know, which throw the sand about and outline the areas of least motion where the sand settles. Figures can be produced which will correspond to the fundamental and partials of the board although in the case of the free vibration the partials will be thoroughly inharmonic. In the case of the forced vibration imposed by the string, with its markedly harmonic characterics, at least relatively speaking, the Chladni figures or eigenmodes, as they are sometimes referred to, will be markedly different, once again reflecting the passing, reflection and superposition of stress waves, that is the sound, in the board. But, in my opinion, in both cases they are nevertheless examples of Chaldni figures the difference being merely those arising from the nature of forced or free vibration. If by 'modal analysis' one means only the case of free vibration then I can see how it could be said that this is not of much importance, except, as Steingraeber appears to do, by using it to evaluate the flexibility of the board around its points of attachment. I think, actually, if what you say about a line of sand appearing along the bridge is true, then this would suggest, as I have maintained that the motion in the area of the bridge perhaps has been minimized to the degree possible, or is minimized by the design. You may have intimated a simple way to test the question of the bridge moving first or subsequently to stress concentration as I maintain or, at least, whether the nature of such motion is essentially at the frequencies and relative amplitudes in the wire, which I doubt. In either case, it suggests again, the the utility of a relatively immobile bridge, at least partially, and, at least, to my mind. Aslo... The fundemental frequency mode pictures I have seen never follow > the edge pattern of the soundboard /rim. And it would be a bad thing > indeed if the fundemental mode was so large. I dont believe that > Steingrębers sand gathering proceedure has anything at all to do with > the fundemental reasonant mode... Lot of good a cutoff bar is if the > vibrational modes dont get affected (limited) by it ... or what ? I think this would have to do with the fundamental of the free vibration, if at all and may suggest useful information as Steingraeber appears to believe is the case as it would appear to show that the board is capable of vibrating relatively easily in spite of its attachment. The fundamental of the 88 forced vibrations will be different and I don't know how well the technique used by Steingraeber speaks to this but they obviously believe it to be important as I think it would have to be. . > Chaldni patterns have to do with the reasonant modes of a vibrating > panel. The edge conditions is another matter. Striking the board even once, in the case of a free vibration, will case the board to develop its modes, although they are limited in definition by the energy in the impact and may or may not be very detectable but they nevertheless exist. If there were no boundary condition that is there were no reflection then stress concentration would not occur and the modes of the board, either free or forced would not develop. The stress wave would simply dissipate as it progessed in the medium further and further from the point of impact. Striking with a harder impact produced either by a harder hammer or one with greater kinetic energy will make them stronger, as long as reflection exists, as will increasing the efficiency of reflection coefficient itself. Striking repetively will also cause them to become stronger as superposition is increased and striking, best of all, at a resonant frequency will cause their greatest definition as superposition and stress concentration will be at its most efficient level. A "modal" hammer attempts to do this but any hammer or source of impact and subsequent stress wave, would, in fact, do. Shaking a bucket of water at the right frequency will show similar superposition and stress concentration. If done at the right frequency for the size and shape of the container standing areas on the surface of the water will be easily visible and this is exactly what happens, except in three dimensions, in a soundboard where dilation of volume and distortion or bending both occur. Regards, Robin Hufford > > RicB > > Richard Brekne wrote: > > > > Delwin D Fandrich wrote: > > > > > > > > > > > > > No... Banging with a hammer or something on the bridge to see where sand > > > > gathers has nothing to do with Chladni patterns. > > > > > > > > Of course these are Chladni patterns. What do you think banging on the > > > soundboard with a hammer or something is doing? > > > > The subject matter at hand is the gathering of sand around the edges of > > the piano. The Chladni patterns reflect the vibrational modes of the > > soundboard. > > > > > > > > RicB > > > > > > > > Striking an object with a carefully calibrated steel hammer is generally > > > how vibrating energy is set up in an object under test for a modal > > > analysis. It's then called a modal hammer and its price goes up by an order > > > or two of magnitude. > > > > > > Del > > > > > > > > -- > > Richard Brekne > > RPT, N.P.T.F. > > UiB, Bergen, Norway > > mailto:rbrekne@broadpark.no > > http://home.broadpark.no/~rbrekne/ricmain.html > > http://www.hf.uib.no/grieg/personer/cv_RB.html > > _______________________________________________ > > pianotech list info: https://www.moypiano.com/resources/#archives > > -- > Richard Brekne > RPT, N.P.T.F. > UiB, Bergen, Norway > mailto:rbrekne@broadpark.no > http://home.broadpark.no/~rbrekne/ricmain.html > http://www.hf.uib.no/grieg/personer/cv_RB.html > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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