sounding board structure and displacement

[Mark Kinsler]

I believe that a sounding board has a set of parallel ribs that serve to 
strengthen it and, in some cases, to preserve its dished shape.

So there are two cases to consider:

If the ribs are perpendicular to our line of sight, then the cross-section 
of the structure will be a beam whose ends taper down.  Presumably the glue 
is secure and has the same flexibility as the wood.  When the center of this 
beam is loaded, it will bend like any other.  Since the center of the beam 
has greater depth than the ends, the beam will tend to remain fairly 
straight, with perhaps the majority of the bending taking place near the 
ends.  The ends would tend to curl up.

If our line of sight is parallel to the ribs, then our cross-section 
resembles a thin arch (the thickness is that of the sounding board) with a 
few lumps beneath it.  When this is loaded at the center, the ends will tend 
to spread out.

Thus the 'action' of the sounding board varies depending on your point of 
view.  Presumably the sounding board doesn't care much.

I believe that the bridges lie near one edge of the sounding board in most 
instruments.  This would tend to reduce the flattening of the sounding 
board's crown.

The purpose of the 'downbearing' in bowed string instruments is to hold the 
bridge in place, hold the strings in place, and to ensure that the bridge 
thoroughly defines one end of the vibrating string.  Perhaps this is also 
the case in pianos.

M Kinsler

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