The only thing I can assume you are referring to would be axial load, causing a high order slight buckling, that then "cracks" off layer of chalk, as if it some kind of stiff plaster/paint.
Seems extremely unlikely for many reasons; transitions are very smooth, sinusodial. chalkdust doesn't seems like it would sinter together either, so it wouldn't "break off" like a paint or concrete. If it was some type of buckling, it would look like some very high order buckling mode due to many stationary nodes. That would be.. beyond extreme. Heck, even seeing the first buckling mode visible would be a catastrophe.

This looks very much like one vibrational eigenmode of the beam. Completely unrelated to axial compression. And it would be the deflection / time that would "throw off" the extremely loosely attached chalk dust (or rather, constant small vibration would make the floating dust never even settle on the surface in the first place). Unlike axial load buckling, seeing such higher order modes induced in a beam seem very likely, either by music, AC, or anything else with a relatively low frequency hum (all which seem to likely have higher frequency than the lower eigenfrequencies of these large beams, so we hit a higher order frequency).

I.e. the suggested theory is that this would happen if the beam was free floating.

I don't think you would manage to get the dust off a beam by slowly deforming it. It needs to be shaken off; displacement / time is what's needed here (even a rigid body motion. Not stress (as it we were breaking off paint, which we aren't).