Modulus of Elasticity

[Richard]

I would like to add a few more thoughts about the
discussion on soundboard rib reshaping. First a small
disclaimer… I know very little about piano soundboard
design and all the issues relating to materials,
shape, mass and stiffness. My exposure to plate
vibration is strictly with aircraft modes of vibration
as it relates to flutter. In aircraft design we try to
eliminate or dampen those frequency modes that are
excited by random air turbulence. If these frequency
modes were not reduced or dampened catastrophic
failure can occur either due to large amplitude motion
or material fatigue. On aircraft we can’t take a roll
of felt or a few mute wedges and stick them here and
there to dampen the vibration. We are usually limited
to just a combination of two things… change the
stiffness and/or change the mass, thereby, moving the
modes of vibration somewhere else where they are not a
problem.  

So what am I getting at? It seems to me that just
maintaining the soundboard rib stiffness is not the
complete answer, you need to consider the change in
mass too. You will need to add less wood to the height
of the rib to get the same stiffness… less wood, less
mass. With less mass you have effectively changed the
soundboard mode shapes and moved the modes of
vibration somewhere else. This change may or may not
be a problem but something to consider. It may be that
the change in rib mass is not a significant soundboard
design parameter, perhaps someone else can shed a
little more light on this issue. In any case, it will
be very difficult to predict changes analytically. The
variability in individual wood properties from the
average published values are probably significant
enough to make even complex analytical solutions
suspect. Anyway, just my two cents… 

Regards,
Richard Yoakum



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