I had a similar problem with a Duo-Art grand.  The solution was far
more simple than some of the other suggestions made here: the legs are
loose.  If there is any give at all where the piano meets the leg, the
piano will shake.

Try tightening all of the screws that fasten the legs to the piano.
You may find one (or more) screw is stripped or has simply come loose
over time because of temperature and/or humidity changes.  You'll need
a extra-wide, heavy-duty screw driver to really get them tight but I'm
certain that this suggestion, at the very least, will improve matters
if not remedy it altogether.

Adam Aceto
Burbank, California