Damping
If we use an electrical analogy, the damping will determine the width of the peaks when we measure the resonant frequency of a component. It will also determine the rate of decay when we ring a bell.
We could put a piezo tranducer at one each of a rod of our material. Put a signal in one end and display the signal at the other. Then sweep the frequency from low to high. Plot the signal amplitude as a function of frequency. The peaks we see will be the resonant frequencies of the assembly. Materials with low damping will have narrow peaks. Materials with high damping will have wide peaks.
Instead of applying a sine wave at the input, apply an impulse. The output signal will be a pulse if the material is well damped. If the assembly is under damped, there will be a decaying sine wave.
The various resonant frequencies will depend on the dimensions of the sample, the speed of sound in the sample, and probably lots of other things that I am ignorant of.
If all you want is comparative information, that should be pretty easy to get with simple apparatus. Quantitative info is harder to get without calibrated transducers.
[This stuff is off the top of my head. It might be partial or total BS. Feel free to tell me so. In fact, I insist.]
Ken
Kenneth Lerman
55 Main Street
Newtown, CT 06470