I opened a similiar thread on here about enclosure materials and didn't really get much of a response. Since then I have done a lot of research on the subject.
An enclosure shoule be stiff, massive, and damped. Stiffness raises the resonance of the wall vibrations. This is good because higher frequencies take more energy to produce from a cabinet, they do not penetrate the walls as easily and because they can be better damped with stuffing materials.
Increasing mass means it is harder for your walls to vibrate and create noise, but with the size of most subwoofers weight becomes an issue quickly.
Damping isnt so easily explained by a novice such as myself, but the concept is that sound energy becomes heat energy as it moves through the medium. Of recent interest to me is viscoelastic damping, in which a thin sheet of rubber seperates two stiff walls. This is most often employed with metal, which is stiff and has a high resonance. Ihe idea is that as sound excites the two sheets they sheer against each other while the rubber tries to hold them in place. The vibration turns sound into heat in the rubber.
Having said all of that, each material has its own resonance. I am really not an expert here but I found one study, which concluded that while plywood and MDF were similiar in stiffness and resonance points, the plywood stopped resonating faster and its resonance point increased more with stiffness. As they put it, the decay of the sound was faster. If sound is going to leak through your cabinet walls, at least it should leak through in an uncolored way rather than all blurring together into noise.
Mdf likes to resonate at about 160hz even if it is made stiff by increased its width, so you end up with a heavier box for little gain. Since there are air voids in particleboard and plywood, the fibers inside them that may be of different resonances can move on their own a little, which spreads the resonance of the material out a little. MDF has no such voids, and moves as a whole. Everyone who wrote in to my thread told me to use MDF, but none of them could explain why.
Good plywood is stiffer than MDF. Naysayers on this forum may allege otherwise, but I have experience in the forest products industry.
If you are a good wood worker, you might consider using a species of pine. The same weight of spruce or fir is much stiffer than MDF. You could use purpose made metal braces on the corners, and the cost would be reasonable. Thickness could be an issue, as you will want to go thicker with the less dense pine. Howard Hughes built the spruce goose out of spruce plywood, not MDF. The parts express featured project "the woody" doesnt look so bad for being pretty crude.
You may also consider HDF or hardboard. It will be variously advertised as masonite, duraboard, etc. and sold as subflooring, "green board," or moisture resistant paneling. Hardboard is a heat pressed particleboard which doesnt use much or any glue. It is very dense and stiff and easy to work with. If you went with hardboard you could have several panels and use an adhesive in between them to achieve a measure of viscoelastic damping. It would also allow you to use a thinner front baffle in order to cut down on reflections from the lip of the baffle cutout behind the woofer.
I used MDF (I bought it before i got wise) covered in fiberglass from a fiberglass kit in a speaker to achieve stiffness.
You could also go to builders square and buy eight feet of rebar for like five bucks and simply liquid nails it across the middle of your panels.
Either way, brace it like you were building a bridge to increase stiffness. Oddly, it seems that when a cabinet vibrates the whole thing vibrates, not just the middle of the panels, so mass would help even a very stiff enclosure. The panels may be of different sizes and resonances, so one panel may be moving in a different direction at a given time than another. Bracing would help this.
Leftover ceramic tiles could be dropped in between layers of wood. Ceramic would be ridiculously stiff.
If youre a good woodworker, dovetail joints glued together with rubber caulk would provide both strength and damping.
pretensioning the walls raises the resonance of the enclosure too, so bow the walls out with a clamp before you put your braces in.
You may also want to mount your woofer on a bead of silicone to reduce vibrations.
Since your enclosure will be so well built and will not have any resonances in the bass range to interfere with your speakers sound, stuffing the enclosure with fiberglass insulation will help you damp out higher frequencies. This will increase the apparent volume of your speaker, too, so be careful or read up. You could also stuff with foam or roofing paper or felt. I like the long strips of light, glued up felt sold as roofing/weatherstripping product. Ive seen it about a half an inch thick. The point is to damp reflections from the cabinet walls. (sorry if you already know all this and im wasting your time.)
Next time I make a speaker I will use a few layers of hardboard with a thin layer of silicon or acrylic latex adhesive between the panels. Good luck!