They certainly work.
The gym I use has several of them.
The vibrating plate creates instability in whichever body part you are working, and your muscles are forced to compensate by contracting repeatedly. It's hard to find any other workout situation that does this so effectively. It leaves your muscles feeling really tight, especially your tummy.
I don't know if the personal machines work as well as the commercial gym machines, but I don't see why not. The principle is the same.
JJ x