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The issue of aerodynamics comes into play as well. Baffle grills, coverings, reflected sounds all play a part in the sig.
I think you can probably use a small mic and put it in contact with cups, headband, and other parts to get a fair determination of what the largest culprits would be.
My concern with some measurements is that they may be inaccurate or not even relevant to the key issues. Also the equipment needed to do this well is quite costly. I have worked in or around engineering or acoustics labs and the equipment costs are huge. Certainly I expect companies like Sennheiser, Phillips and possibly even Grado to have some of this. As I have mentioned, Sorbothane doesn't seem to offer much data on their products or do much measurement related to these issues.
In the end you are concerned with the sonic product the ear or microphone actually picks up but you need to tease out what the mechanical vibrations are doing to this sonic product as distinct from the airborne reflections coming from the parts you mentioned. As well there are resonances in the air chambers of the headphones and physical characteristics of the drive to consider.
Another technique which might help is what I think are called "waterfall" graphs. I have seen some, which looked at the decay of impulse sounds over a few milliseconds. I think zolkis was referring to these.earlier. These don't directly tell you what is going on due to vibrational issues since they pick up all the delayed signals. However if you compared plots from damped vs undamped systems you might get some clues as to what’s going on although it wouldn’t give you definitive answers.
Ultimately, I think you need a different kind of sensor than a regular microphone to tell what sort of vibrations any part of the earcup is undergoing. And even then, if you had a sensor which you could directly attach to portions of the earcups it would need to be heavily insulated to keep airborne signals from getting to it and contaminating the results.
All in all, I don’t think this is an easy problem to understand or solve and it seems to fall more into the realm of mechanical rather than electrical engineering. However most of the people working in audio, seem to have an EE background. I recall reading a post from a mechanical engineer in another forum who was quite caustic about theories put forward by audiophiles and EE types about mechanical type issues in audio. He was saying that they had come up with their own version of science unmoored from the real thing. In my opinion, much the same could be said about the psychoacoustic discussions on these forums.