Transformer is a static device. So mechanical motion in a transformer is very little. Some small vibration occurs due to humming and other effects. But power loss due to them is negligible compared to copper loss and Iron loss. But for a very precise operation they may be considered by suitable modelling. Please refer to M.G. Say's book on A.C Machine, this issue is well addressed there
As there is no mechanical rotation in transformers, no mechanical losses exist. the vibration of the core lamination does not cause significant mechanical losses.
The transformer is a static device and therefore, the losses as a result of movement are minimum, the transformer will generally experience losses as result of the magnetic characteristics (Hysterisis and eddy currents losses), winding characteristics (ohmic, hysterisis, eddy and stray losses) and structural losses (tank, frames, etc).
The changing magnetic field at the heart of transformer operation drives magnetostriction. Magnetostrictive losses in typical core materials are small enough compared to other loss terms to ignore for most purposes. However, at power frequencies the hum generated can be annoying.
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