Materials to reduce sidewall flex & vibration ?

Spoken like a dealer.

Then don't buy new speakers, buy used ones on Audiogon. 

Hello rotarius. I appreciate your suggestions are very relevant so likely you
have some knowledge. Do you have some more specific suggestions? Thanks.

It's hard to be specific because induced vibration and resonances are so dependent on the masses coupled together and the natural frequencies of all the materials of a given system (speaker).  At work, I have access to vibration analyzers, so if I had to attempt an experiment like this, I would use some equipment to quantify the results.  Like someone suggested earlier, you could use materials that dissipate vibrations in the form of heat on the inside walls without much thought.  Just because something you stick on the panel is very rigid, it does not guarantee anything.  I mean it will still transmit vibration and it will resonate at some higher frequency. Is that better for your sound? 

Thanks rotarius. I very much respect the benefits of measurement with equipment; but it's not available to me.. You mention " you could use materials that dissipate vibrations in the form of heat on the inside walls without much thought ". If so, why could the same materials not be used on the outside? I'm simply looking for the best material for this. So far it seems like an epoxy with fillers of fiberglass,carbon fiber and lead slivers to both provide rigidity and dissipation of vibrations by turning them into heat. Your thoughts?

Well, for one thing, stuff like Dynamat, norez, etc. would look ugly on the outside! Your aim should be to minimize the excitation of vibration of the speaker walls so the material you use would ideally be placed between the speaker wall and the source of the excitation. I suppose there may be something to gain by sticking them on the outside.  I am just not sure if the effort is worth it all but hey, if you like tinkering like me, that's half the fun.