FWIW,
The machine doesn't shake ( lets use the term vibration ) when nothing is turned on. When the motors are turned on the machine may vibrate.
So the machine is sensitive to a range of fundamental frequencies. The machine will vibrate if a fundamental or some harmonic is near the machine / some part of it is near it's natural frequency. Should things be just right the machine can go into resonance and that you would surely know.
So there are a mechanical considerations to this and from a machine point of view vibration is being induced by the motor system.
If you accept that fact then look at the motor system to eliminate the machines vibration problem.
Curing one axis provides solution for the other axes.
Consider.........
What are the motors doing when just turned on but the controlling software is not providing servo control?
What happens when the servos are getting control instructions?
Noise / EMI can be seen as the equivalent to receiving software instructions.
Here a link to info on EMI:
http://www.machsupport.com/forum/index.php/topic,25616.0.htmlRICH