For subwoofers, it is not an issue. You can easily use any conventional material, and with moderate bracing, push the resonant frequencies of the panels above the bandwidth of the subwoofer operation.
For the mid-range, though, this becomes a real issue. There is no way to use normal materials in a
practical capacity and push the resonances of the panels over the bandwidth of the speaker system. It can be done - but it would require extraordinary building techniques.
So, normally, you will use a system that reduces the amplitude and converts the vibration to heat energy as efficiently as possible. The most practical method, using normal materials, that I have found in my testing: 0.75" high grade cabinet ply, then a constrained layer dampening adhered to this. Dynamat for example, in layers built up to 1/8" to 1/4". Then adhere solid oak, 1" to 1.5" to the Dynamat. Now install braces in every axis(X, Y, Z), and thave those braces spaced not more than 3" from another brace. This means a very dense bracing content in the cabinet. However, this method will result in extreme low level cabinet panel output.
Here is an example of a small bookshelf speaker using conventional MDF construction(Ascend CBM-170 SE), compared to an enclosure using the method described above. This measurement was taken with an acellerometer attached to the center of each bookshelf speaker's side wall, and both speakers driven to the same measured SPL:
The cabinet construction I specified has up to 30dB reduction in output compared to the standard cabinet.
-Chris