Material properties

Here we want to document some material properties we use in design and analysis of what we build. It was very useful to do this: It forced us to sort out errors and inconsistencies. We are sure there are plenty left.

First off are flat plate properties needed to predict what a simple box, actually a cajón, will sound like. This is a good example of something that can be modeled as a set of interacting (in this case two) oscillators, and a model by Christensen and Vistisen is relevant [Christensen and Vistisen, “Simple model for low-frequency guitar function” J. Acoust. Soc. Am. 68(3), 758-766 (1980)].

These oscillator model(s) need plate input parameters, which can include the fundamental frequency, its dependence on added mass, stiffness, effective mass, and effective area. These in turn are dependent on wood properties, and wood orientation. So here we document for our later reference some useful (to us) equations and values. Note we are not considering arched or braced plates, only flat plates that represent the situation in the cajón. We really want to consider orthotropic, clamped, rectangular, flat plates, but we also consider some combination of circular, elliptic and isotropic plates as well, to gain insight and check consistency. It’s easy to make mistakes.