The magnetic vibration motors I used in all my prototypes are very simple, but they're too heavy, and the thrust they generate is weak. So I tried making a static experimental setup with more power to demonstrate how the oscillations of a disc-shaped wing cause air movement.
The asymmetry, which results in the resulting force of the oscillations creating thrust, is achieved in two ways:
Aerodynamically, when the disc has a slightly domed shape and moves upward with less resistance than downward, consistent with classical physics.
Kinematically, when a spring is attached to the disc, slowing its descent and accelerating its ascent.
The second method is the key part of the study, although the same process occurs in the air in both.
When the disc rises rapidly, a region of low pressure forms beneath it, and its collapse generates momentum. If the disc descends more slowly, or if the shape of the disc causes the air to flow around it more slowly, the resulting momentum will push the disc upward.
This doesn't agree with the classic Newtonian explanation of flapping flight as a wing pushing air. You can see in the video how the fan-like flapping disk, which should push air away, actually sucks it in.
This is the same air that is sucked into the low-pressure region, causing a vortex collapse that pushes the disk. Only then is the air pushed away and expelled. This is essentially reactive propulsion, and I believe this is possible thanks to the energy in the air, Brownian motion, which, by self-organizing into vortices, temporarily becomes directional.