Most excellent. This is progress in the right direction. You are saving me a whole bunch of work at the keyboard, and this should read very linear. I will dispense with further questions, and provide my 2 cents on the issue. My basic overview is thus:
"You can't have yer' cake and eat it too".
I tend to think that a reasonably light and stiff material with good internal damping will have a low enough magnitude in the out of phase areas that it won't cause major problems.
It sounds like you are middle of the road guy with some tolerance for flexible cones. This is fine. I certainly understand the advantages for a simple crossover design.
So the voice coil is attempting to move at 20 KHz. The area of the diaphragm closest to the voice coil will follow along. The farther you get from the voice coil, the less the diaphragm immediately follows the voice coil. You get areas where the diaphragm is out of phase or even in anti-phase.
A very good actual example of this is exists in the response curve for the W18E driver on the SEAS page. The surround material thickness and type determines the response slightly above 2500hz. The relative dip between 2500hz and cone resonance at 4200hz is the surround material moving out of phase with the driver. However, this also means that the CONE of the W18 driver remains a piston up to this frequency range. The stiff edge of the cone at high acceleration pushes the surround into "whiplash".
By converting it into heat.
Yep, the only way the well damped material can convert the sound energy into heat is movement. Insulation fibers are the easiest to understand in this regard. The do flex when encountering sound waves, and do certainly convert the energy into heat. What's critically important here is that the dampening material MUST FLEX to convert the energy into heat. Again, the material must flex to convert the energy into heat. This truth is critical to this discussion.
Herein, there is are of trade-offs.
Flexible materials produce flexible cones, but will soak-up the internal resonance inside the cone, and allow a shallow slope crossover.
Stiff materials produce stiff cones, but will NOT soak-up the internal resonance inside the cone, and necessitate a steep slope crossover.
There are further trade-offs in cone shape.
Curvalinear cones are more flexible, and push the cone resonance higher.
Straight sided cones have more rigid, but the the cone resonance is lower.
Probably the most credible public example was present on the SEAS web page. SEAS published the distortion graphs of the 8" Excel metal cone driver and their 8" Excel paper cone driver. These drivers used the same motor, same frame, same voice coil, and different cones. The cone weight was nearly identical. The measured distortion from these graphs was significantly different. Starting from about 100hz (yes, 100hz) the paper cone driver had significantly more distortion. Unfortunately these graphs are no longer present. I don't know of a current parallel example.
It might seem possible to have a stiff cone that is also well damped. I have encountered ALMOST such a cone. The SCC300 driver has a VERY thick paper cone with a VERY hard coating. To the touch, this driver is very stiff. To the touch, this driver is seems very well damped. Indeed, this cone was done very well. It has a nice peaky cone resonance around 800hz - just like a metal cone.
I believe the primary issue with stiff cone resonance is NOT what happens when the voice coil pushes the cone too hard at higher frequencies. I believe the primary issue is the buildup of acoustic energy INSIDE the cone at higher frequencies. As the wavelength of the frequency generated by the cone becomes slightly shorter than the diameter of the cone, it will resonate inside the cone. The soft cone will absorb these frequencies. The stiff cone will not. They will reflect immediately from the cone surface into a plume of nasty grunge. Such is the case with ALL stiff cone drivers I have encountered - SCC300, Accuton C95, SEAS W18E, W18EX, Focal 8k, Seas L17, L18... . Caviat, some of these drivers do have compromised curvalinear cone as mentioned above.
I feel compelled to mention there are better cone materials and worse cone materials in their respective categories. Certainly these can be objectively evaluated. However, find my subjective ear is darn keen, and follows the distortion measurements. I believe my current cone material favorites are ceramic (very recently), and paper.
The summary...
If you want the cone of a driver to "stop on a dime", it's gotta' be stiff, and it's gotta' reflect sound energy. It will have a resonance.
If you want to use a 1st order acoustic crossover with a 7" driver at 2500hz, that cone needs to have flexible material, in a flexible cone to absorb the sound energy. It won't have resonance.
Whew, that was long. I am going on vacation for 2 weeks this Sunday, and will not return to this issue until the end of July if needed.
Dave