I didn't get the training on materials engineering. But isn't it just proposing a complicated, costly if not sophisticated solution before analysing the problem? Is there a problem at all? If so, what is it actually? Might be that one needs an argument to sell an otherwise mediocre design by excellence in carpeting. That can be had cheaper I assume.
How could You know what I might recognize as objectionable? One could derive some parameter from measurement and compare to something else. But from experience such simple computation of data regularly doesn't hold true with physiology, let alone with, say 'taste'.
My observations:
- the resonances seen with knocking are already well damped in conventional designs (MDF etc), concluded from how broad they appear (calc/ 'Q')
- when driven by the speaker, the peaks in the acceleration of a cabinet wall never correlate with resonances excited by a 'knocking
- when driven by the speaker, there are never higher modes in that the panel showed phase differences from one measuring position to the other, and the amplitude of acceleration steadily decreases towards the rim
- when driven by the speaker, the frequency of peaks does not change with stiffening the panel on its own, neither with adding mass to the panel
- when driven by the speaker, the peaks in the acceleration of a cabinet wall correlate with expectable air column resonances
- when driven by the speaker, the spectrum of peaks is harmonic ( 1 .. 2 .. 3 .. ) as expected from air column resonances ( while panel resonances would show a quite irregular spectrum e/g 1 ..1,4 ... 2,7 ... )
- when driven by the speaker, the amplitudes of peaks decrease significantly up to vanishing utterly with dampening the internal air volume by e/g some highly effective Basotect material
You can derive Your own conclusions in the very unlikely case You trust my experiences. I've gone through it, me thinks, using two accelerometers on a twin-head amp and analyser.
My personal conclusion is that most of the panel's acceleration is due to internal air resonance.
Practically the enclosure shall be stiff by internal bracing to begin with. It doesn't suffice to point-connect opposing walls, because the phase of internal air resonance has opposing phase between the panels. Otherwise the panels may be made of 12mm (1/2 inch) MDF to fully comply to needs. Further crucial thing to do is to dampen the air inside strictly, even if a resonance would not show in the membranes output directly. If that eats up bass, just make the enclosure larger.
By the way, somebody measured the panel's contribution already with a deliberately bad design. He used the Green's Function to separate the membrane's and the panels' part at a distance--it was an engineering thesis addressing the mathematics, not the actual speaker. The panels' contribution was found to be tiny tiny at best (or worst, as You may see it).