Thanks a lot Iacopo. That must have been lots of work. It seems that you have definitely established that it's a resonance effect.
I thought about it, and it seems to me that if it was spinning at the same time as vibrating, and at the same frequency, the disk center (where the rod attaches) should go around a circle two times per each turn of the wheel (like a figure 8 but folded in half) but I'm not seeing it in the slow-mo video
Thank you for your input, I would have not thought to whirling by myself.
I learned more than expected from this little experiement.
Maybe I found something other:
Maybe the lack of vibration is not an issue because the rotation itself could be the vibration.
Depending on how I start the vibration, I can make the rod to oscillate back and forth, but also I can make it to oscillate making an ellpise, or even a circle, instead of making a back and forth motion. So maybe rotation and vibration are not so different things.
I tried measuring the frequencies of the rod oscillating back and forth and of the same rod oscillating in circular motion;
The frequency doesn't change, is the same.
But, at this point, I have to admit that Jeremy was right.
If the constrained rotation of an unbalanced mass can produce whirling, the unbalanced top can whirl.
The constraint, (the rod, in the umbalanced disk, trying to make the disk to rotate about its simmetry axis, instead of about the CM), in the case of the spinning top, is the tip:
if the CM is at the same height of the tip, (a spindulum), and the top doesn't slip, the CM has no freedom at all to move horizontally where it wants and is constrained to simply spin about the tip. This would be the equivalent of the stiff rod situation in the disk.
This makes the applied force to have an effect in its same direction.
The heavy side of the wheel with a stiff rod moves outwards, centrifugal force.
The heavy side of a spindulum sinks down, gravity.
If the constraint is weak, (soft rod in the disk, CM far from the tip in the top), and the speed high enough, the effect of the direction of the force becomes shifted by 180 degrees; the heavy side goes towards the rotational axis, both in the top and in the disk, and not outwards, as expected for centrifugal force to behave.
It seems that there are overlapping concepts in the literature of whirling and in that of a mass wanting to spin about its CM, the second maybe could be in some way considered a case of whirling.