Well, I was hoping to see some responses over night because you have a curious phenomenon going on. I do not believe it is water hammer which is good as that type of vibration has some serious forces involved.
Is your drain pipe corrugated on the inside or does it have smooth walls? How long is it and are there any joints underground.
My 2 cents suggests that it is the gulps of air that are rattling along the corrugations. If that is the case, I would be concerned about any underground joints you might have, but without joints, the vibrations cold be helping to settle any loose fill and actually packing the pipe. IDK, just looking on the bright side.
Hopefully adjusting your anti-vortex plate will prove to be an improvement.
