I just checked mine. I never noticed a vibration before, but putting my hands on the sides and top today, I could feel a low level vibration, almost like a back massager pad on very low.
I have never noticed it moving, and it has run for several hours at a time. But it has been on surfaces like the MFT and a plywood shelf. I don't know if it would shuffle around on a glassy smooth surface, but I would be surprised if it did.
By the way, when I have turned it on and then moved it to a different location, I never noticed any vibration.