Cut off bars and resonant frequency

[Richard Brekne]

A key passage from Wogram (below) relating to the effect of effect of 
the resonant frequencies of the soundboard.  How the positioning and 
size/mass/stiffness of the cutoff bar would affect a given panels 
resonant frequencies in general I am not sure of.

Cheers
RicB

> "No uniform relation was found between the successive stages of 
> reduction of the rib height and the changes in the input impedance. 
> The influence of the first reduction (from 100 to 75% rib height) was 
> considerably less than that of the second (from 75 to 50%). The 
> influence seems to be greater once the basic stiffening has been 
> removed and there is no longer any compensation for the anisotropism 
> in the moduli of elasticity.
>
> Turning to the sound radiation, the same effects were observed as for 
> the impedance; the lower resonant frequencies are shifted downwards 
> and sound radiation is reduced. However, unlike the effect on the 
> impedance, the reduction in sound radiation extends over the entire 
> frequency range, even above 500 Hz. This is due to a short-circuiting 
> phenomenon, as mentioned in the introduction. Above a certain 
> frequency, the soundboard no longer vibrates as a unit but divides 
> into a number of vibrating areas, which results in a poorer radiation 
> efficiency. In addition, the lack of compensation for the anisotropism 
> causes a reduction in the total vibrating area and hence a poorer 
> radiation.
>
> From the measurements it can be concluded that the two most important 
> functions of the ribs are to stiffen the soundboard and to compensate 
> for the differences in bending stiffness parallel to and across the 
> grain (anisotropism). The bending stiffness exerts a greater influence 
> than the mass. For this reason it is more advantageous to use narrow, 
> high ribs than ribs with a low and wide section."
>