We have a location near a railroad line and when trains go by the vibration seems substantial enough to possibly cause (or explain) harddrive damage.
I wonder if suspending a machine or hanging it in some fashion might alleviate the problem, because we need something inexpensive. However, that might not actually do enough to dampen the vibration. Has anyone tried anything similar? I was thinking short rubber strapping attached under a desk or shelf.
Might this work? Or is there something inexpensive to consider instead?
You're going to run into some fairly serious safety issues hanging any kind of enterprise-grade server on rubber straps, not to mention issues with serviceability and such. Look to some of the seismic and sensitive equipment gear to provide some kind of mechanical isolation for an entire equipment rack rather than an individual component.
A cursory search turned up a few decent options something like this - http://www.starcase.com/isolation_mounts.htm - seemed like a relatively inexpensive way to approach the problem, assuming the specs agree with your requirement. You'll need to be very careful about loading characteristics and if the rack in question is also secured on top then you'll likely require isolation on these connections as well.
Ultimately, however, the right (read: not cheap) answer would be to consult with someone who deals with these kinds of issues (harsh environment / seismic ratings) professionally. I would start with the major rack vendors (Chatsworth, Panduit, APC, etc..) as they've likely dealt with this kind of situation before.