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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