If it was up to me, I'd make a box from 3/4" plywood with a cross member in the middle. That is, a minimal torsion box. If you really want heavy and vibration proof, get a bag or two of play sand and put it inside. Sand is a very good vibration absorber.

Thanks, Bob. So what would you frame the box with?

3/4" plywood all around. You can do whatever joint you want on the corners, butt, miter, rabbet, tongue & dado, etc.

Again, if I was doing it, I'd probably miter the corners and stick in some biscuits. If you don't have biscuit cutter, then maybe either a spline or simply an internal glue block.

If I was more interested in getting it done than appearance, I would simply butt the sides together. You can also get iron-on veneer edging to cover the plywood edges.

OK, thanks.

I'd build it like a fish tank stand. I'd use pressure treated 2x4s to make a frame, then 1/2" ply for the sides. I'd leave the top and bottom open.

But, I tend to over build.

Thanks again to all who posted, but we may close this thread now. We've decided to go without the pedestals because we want a usable shelf or counter over the machines, and pedestals would make that too high. Plumber and electricians are working as I type, and machines will be delivered next Tuesday. I will post a thread about the completion of our closet laundry in the Laundry Room forum at some point after all that happens, if anyone's interested.