The so called beat frequency is sensed more by the human ear than the airframe.
This whole phenomena is about perceptions of the human ear and while likely associated with something spinning in the innards of the airframe it is very unlikely to be associated with causing any kind of damage to a critical aircraft structure.
Loth that I am to wander - as a non aero engineer - into the halls of the knowledgeable, to say nothing of the experienced, but I'm not sure you can go quite that far sir.
It is true that the human ear is incredibly sensitive to sound and in particular to
changes in sound. Even with my somewhat degraded and abused hearing, I can and have heard a change of less than a half Herz in fifty and, I suspect, could probably hear a change of a few tens of rpm in a couple of thousand.
I think where I have a problem is with the sheer mass of either rotating parts or, more probably, the air being moved by these huge donks. A friend of mine supplies quality sound equipment for professional 'gigs' and I watched him 'running in' a couple of speakers each about the size of a Mini. He had placed them 'face to face', up tight, in his living room! He was feeding an out of phase 'beat' frequency into them, at pretty much the full output of his amplifiers which, I can assure you, can move your internal organs.
However, virtually no sound could be heard. Move one of them, at an angle, an inch away from the other and the furniture started to move.
If a beat can be heard in an aeroplane, it means that the vibrations created by one engine are not being cancelled by the other and that energy
may be being absorbed by the airframe. Could this not produce stresses in the airframe, particularly if the perceived beat frequency hits a resonance?
As an engineer, it just seems rather ........
improper in some way,
not to synchronize engines if it is possible. Untidy if you will?
Roger.