Modulus of Elasticity

[Ron Nossaman]

>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. 

* Hi Richard. We can't on a soundboard either, but we can add weight.

>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.  

* The idea in soundboard design is to specify and control the frequency
response and mechanical impedance of the assembly in any given part of the
scale. Resonant frequency goes up as the assembly gets lighter or stiffer,
and impedance goes up as the assembly gets heavier or stiffer. You can
drive an assembly at a frequency that is lower than it's fundamental
resonant frequency much easier than you can drive it at a frequency above
(to a point). From that standpoint, the mass of the assembly should be kept
to a minimum consistent with required stiffness. The stiffness can then be
controlled with rib dimensions so that the assembly is very stiff (high
impedance, high resonant frequency for fast energy transfer from the
strings) in the treble, and  more flexible and elastic (low impedance, low
resonant frequency) in the bass. If the assembly proves to be low enough in
impedance for the low bass, but too low for the low tenor in the same
general area of the board, the impedance at the end of the tenor bridge can
be raised by extending the bridge in the design phase to make the assembly
stiffer in that spot, or adding a mass load to the underside of the end of
the bridge.

* It's not exactly pertinent, but can't you control flutter to some degree
by thrust vectors relative to flight surfaces, sweep angles, airfoil shape,
vanes and ridges, or other laminar air flow control?   


>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

In a compression crowned soundboard, you get very little control of the
resonant frequency and impedance. The ribs have to be flexible enough for
panel expansion to bend them from flat, to an acceptable crown. Stiffer
ribs just mean less crown, and don't stiffen the assembly appreciatively
since the panel is doing all the work in supporting both crown and string
bearing. The resulting crown with any given rib scale will vary from
assembly to assembly depending on the wood chosen for the panel. You have
to take what you get because there's not a lot you can do about it. The
physical limitations are built into the method. Rib crowning, on the other
hand, gives you a much broader range of reasonably predictable impedance
control because you can build a light, high impedance assembly, a heavy,
low impedance one, or blend the impedance gradient from one end of the
board to the other to a far greater range, under much closer control, than
you ever could with compression crowning. Rib crowning allows one to make
the mistake of their choice, as it were, or to deliberately steer the
assembly response in the direction they wish. Trouble is, there is no
universal set of rib dimensions or standard deviations from the original
design that guarantees success. A whole lot of factors have to be taken
into account, like with airplanes.



Ron N