The motive force applied by the voice coils is enough to move driver cones back and forth a quarter inch or more in each direction, so it's not hard to see why the pressure generated by that cone movement can make the cab panels vibrate back and forth by 1/32 inch, which is plenty to cause a head to move about. Bracing like that in the thread I linked to a few posts back can eliminate panel vibration, or at least make it so slight that even a ten pound amp won't move around. Thicker panels work too, but at the cost of weight. One brace connecting the middles of a pair of 1/2 inch thick panels is the equivalent of using 1 inch thick panels. Three braces spaced equally is the equivalent of using 2 inch thick panels.
My intent of awakening the zombie thread was to say that my Dually seems to be well braced. If you wrap the panels with your knuckles, they produce a well damped and relatively high pitched sound. Adding mass to the design should further reduce vibrations, but the cabinet's light weight is one of it's strong points.
Some builders offer different construction materials including okoume. I don't know what my Dually is made of, but I can lift easily with one hand and carry it up a few stairs. I wonder if anyone has compared Duallys made out of different materials to see if there is any noticeable impact on tone and vibration.