There will always be a large 2*line frequency (2x60=120hz in usa) vibration from forces associated with the 1xline frequency flux in the core. I believe that vibration will increase as the voltage is increased, since this causes an increase in magnetizing flux.
I've heard the term magnetostriction used to describe the 2xline frequency vib, but I never knew exactly what it meant.
Obviously pumps and fans if running can cause 1x running speed vibration due to imbalance, or harmonics of running speed for misalignment, loosesness, rubbing etc. Possibly also some flow vibration for forced oil.
It is possible that electrical discharges occuring in the transformer can give rise to very high frequency (hundreds of megahz) vibration/noise.
I'm not sure if that's what you're looking for. Are you looking to diagnose transformer problems through vib analysis? Or are you just looking to minimize vibration coming from transformers.
There are two things in trfs-vibration and noise.They are some what interrelated.The main cause as electricpete poined out is magnetostriction in core laminations.As the sinusoidal flux moves along the core,the length of lamination increases and decreases during the +and - of the wave.This is called magnetostriction and occurs at twice the supply frequency.This vibration is transmitted to tank sides and cause sympathetic vibrations and some times cause resonnance vibrations too.
The vibrations from load current ,I believe is from the leakage flux flowing outside the windings through the tank and structural parts of trf.
Vibrations from coolers are normally not so appreciable
