You wouldn't happen to have large and powerful AC units along with refrigrators on that same circuit would you?

A condition known as "dirty power" can possibly cause the effects you mentioned. This is where the AC sine-wave gets heavily skewed from strong non-linear loads. If you have a power-conditioning active UPS you should plug the monitor into it and see if it solves the problem. Or take the monitor home and try it out there. If it cleans up and stops shaking, chances are it is an issue with this dirty power stuff. Some monitors are more susceptable to it than others, usually depends on how powerful their PSU is and the size of it's capacitors, etc.

Anyways, hopefully your next monitor deals with whatever the issue is better than this one.