The STM in a surface chemistry lab I worked in for a while was inside a box, and hanging from the roof of the box. By choosing appropriate springs to hang the sensitive bits from and sound proofing the box, it could adequately isolate the scanning table from its environment.
http://iopscience.iop.org/article/10.1088/1681-7575/54/1/S1/...
I've started searching for "dilution refrigerator" and found this video, explaining a little bit how ³He–⁴He mixture cooling works and what the applications are. I think the video also helps putting the Wikipedia article in a perspective and vice versa.
Quantum Cooling to (Near) Absolute Zero (2013): https://www.youtube.com/watch?v=7jT5rbE69ho
But I don't think this is relevant here.
EDIT: Yeah, pohl answered it. Vibrations are not relevant.