Stiffness measurements
Be warned: You won’t find anything exciting here. It is documentation of what we have measured about plate stiffness. We needed to write it up to make sure it doesn’t get lost, and to check consistency. We have information on individual isolated plates, and on different plates as part of completed instruments: We are working on the same plates first isolated and then part of an instrument. As such this document is work in progress: It will be updated.
One characteristic of archtop guitar plates that is easily measured, as a guide to reproducibility, is static central stiffness. This is, for specified boundary conditions, the force needed to displace a plate location (here the center) a unit distance: Units are Nm-1. We usually use the bridge center location, about the highest point on the arched plates, to apply the force and measure the displacement, although we have also measured the displacement distribution across the plate. We have made measurements on simply supported and clamped isolated plates, and on constructed guitar bodies. We have looked at how different levels of clamping, and brace depth, affect the results. We have some limited information relating stiffness to plate fundamental frequency.
Our current conclusions so far are:
1) We are starting to collect stiffness data on isolated plates and plates on completed instruments. So far the two sets to not overlap: We have only one measurement on an isolated plates that was then used on an instrument. This can be quickly solved using guitar G8, that incorporated the AYC and WRC isolated plates discussed above. Also we are building a guitar using the Fir top and Bubinga back plates discussed above. We will get back to you!
2) Measured stiffness coefficients are “not inconsistent with” the values expected from modeling of the plates as spherical caps. In all cases clamping increased the stiffness, with the limited data showing the largest increase (as a ratio) for the one (Fir) top plate compared to the two (AYC, Bubinga) back plates.
3) Thinning braces on a top plate decreases top plate stiffness, a lot.
4) We need to measure how the stiffness of a plate glued up as part of a complete instrument compares to an isolated simply supported or clamped plate: Where doe it lie in that range?
5) We need a theoretical estimate for an orthotropic simply supported flat plate.