I am replacing the ventilation fan in our master bathroom this weekend. The previous one (about 12 years old) developed such a vibration over time that it managed to undo the bolt holding the glass cover on, causing it to fall and shatter. I haven't removed the fan yet, but it appears to be securely fastened either to the joists or to a mounting kit (it's an 8 inch box, and I'm guessing the joists are farther than that), so I don't think it's just a matter of the whole thing coming loose. Is there anything I can do while installing the new fan to prevent similar vibrations from occurring?
Fan vibration is mostly a matter of fan quality (which unfortunately is not as simple as price, though it's sometimes related.) Bearings and how well the fan blades are balanced are the main influences.
You can also switch to an inline duct fan located away from the bathroom - any vibration would be non-local to the bathroom, at least, and as a general (but not utterly definite) rule an inline fan may be of better quality than most ceiling-type fans.
Pure speculation here, but the theory is solid:
The vibration may have been caused by, or exacerbated by, an imbalance on the fan blades due to a buildup of dust and grime. I've noticed that the intake grilles of bathroom fans, if not cleaned, tend to build up dust. Periodic cleaning of the fan blades (not merely the grille), if they can be accessed, may be helpful.