more on ribs and beam stuff

[Ron Nossaman]

>4. Arched beam with ends clamped. This is the closest you can get to a
>glued-in soundboard with a 1-D model. Here the behaviour is different - in
>response to a local force. Try it. Bend a thin plank arched upwards by
>forcing it between two blocks clamped to the bench. Now push down at one
>side. It is initially hard to push (like #2) then suddenly much easier as
>the other side pops up and it chooses the shape of minimum potential
>energy. A 2-D version like a real glued-in soundboard, even a simple
>square or circular shape, would exhibit the same sort of behaviour
>locally, but more complex. In fact, too complex for simple calcs. This
>would explain Del's observations of a non-linear deflection response to an
>applied force. I would be interested to see the data from those
>experiments Del. 
>
>Stephen
>
>Stephen Birkett Fortepianos
>Authentic Reproductions of 18th and 19th Century Pianos
>464 Winchester Drive
>Waterloo, Ontario
>Canada N2T 1K5
>tel: 519-885-2228
>email: birketts@wright.aps.uoguelph.ca
>


Stephen,

Not really, because the end restraints (case) aren't maintaining the crown
in a real soundboard, and the installed soundboard assembly stiffens as it's
deflected. Here's what I think is happening.

When you lay a ribbed board in place on the rim and apply a little pressure
to the center, it will lay down so the rib ends touch (more or less), What
doesn't touch is the bottom end (tail) of the panel, and usually the front
treble (If I recall correctly). When the board assembly is glued in, the
tail end has to be forced down to the rim with clamps. I know you clamp the
entire perimeter, but the tail has to be forcefully sprung down, where most
of the board perimeter will go down to touch pretty easily. So now you have
the panel adding deflection load to the first few ribs in the tail. When you
load the board, the ribs deflect under load, while the panel is
straightening and relieving the ribs of it's load. The effect is that the
assembly resists deflection more as the load increases. This actually would
happen at both the belly bar, and the tail, since the panel is crowned
roughly perpendicular to the ribs and will resist making the compound curve
necessary to touch the rim all around, so the apparent stiffening under load
would be seen throughout the scale. A good test might be to place small
strips of wood over the rib mortices in the rim, and lay the ribbed panel
in. With the entire panel supported by only the rib ends, load the board
with weights and measure deflection rates. I'm guessing the deflection rate
will be much more linear under these conditions. 

I'm about to start assembling a board for a M&H A. I'll pay attention and
try to take some time to check this out. 

 
 Ron