Materials to reduce sidewall flex & vibration ?

Thanks johnk but the damping spray you mentioned,although it does have its application benefits, will not contribute to my goal of maximizing rigidity..  "I'm curious about fiberglass and other products that can attach/bond permanently to the sides yielding the highest stiffness to weight ratio." So far my research seems to indicate that epoxy filled with fiberglass or carbon fiber,or carbon nanotubes, combined with high mass material is the best option. I continue to research and appreciate contributions.   

Thanks Geoffkait. Yes smart metals have fascinating potential,along with gels that instantly harden upon attempt at deformation, but I feel the momentary time delay renders both non ideal. 
I think constrained damping can be more immediate. Of course I'm just thinking; I'm not a materials scientist---aha--you've given me the idea to search for the 'chat rooms' of materials scientists discussing cutting edge damping materials and techniques. Appreciated.

Thanks soundsrealaudio for your direction. I agree with you and am wondering what materials would do this best.

Just to clarify soundsrealaudio, I am seeking a composite of the 'most rigid' and highest damping' materials to use. So far the filled epoxy appears the most efficient. 

pass
Well sometimes the most rigit is not the best dampening material. Sometimes they just store the energy and release it slowly Not good. If your speakers are vibrating, and most do, then glueing solid materials to the outside may not work out so well. The vibes might possibly loosen the rigid material right off the panels. Imagine glueing a rigid panel to the outside of a clothes dryer. 
Once they begin to loosen you really have a problem. I much prefer my recommendation.