Why do you want to enclose them in cabinets with a built in look. Is this to be in an open space?

I think I'd be more worried about water and steam warping the wood than I'd be about vibration. You need the pan under the washer in case there is ever a leak.

I think if it were me I'd find or build a closet to house the machines.

Servicing the machines would be difficult, I would not enclose them. They are beautiful machines, why hide them?

The laundry is going to be in our newly-renovated master closet/dressing room (no other place...they are now in garage!). Original plan was to have them in a closet, but then the doors to the closet would always be hanging open, impeding access to the rest of the room, etc., so we are planning to have them set off in an "alcove", but no doors. So, since this is mostly "my" space, I don't want the washing machines just hanging out there, looking utilitarian, and with all the associated junk that would be left on top of the machines, etc.. We've gone from putting a countertop over them and upper cabinets, to the idea of having them in cabinetry (but no door on the front of the cabinetry, so the machines will still be accessible (at the front, at least), for a "semi-built-in" look. Contractor plans to put emergency shut-offs, etc. in the upper cabinet (above the hole where the washer/dryers will sit) so we'd still have access to that in case of emergency (and will have pan) with drain for possible leaks.