The question should be asked, though, based on the fact that "equilibrium position" is, however convenient, a complete delusion-there is an intrinsic frame of roughly constant acceleration, not limited to 4d, but some higher ordinality.
Does motion affect other parameters of a body than positional only?
To basic physics, it doesn't, but empirical evidence continues to mount disproving that in very subtle and startlingly obvious ways.
That would be a wonderful topic for a post, that I haven't more than a few brief moments to spend to develop, but perhaps someone else might be able to spend the time.
RE: Vibration - physics explained