What is and is not exact
The mode shapes and frequencies come from the Kirchhoff-Love plate
equation with free edges, solved numerically for this plate’s
proportions and material. They match published values for a free
square plate to five significant figures.
The sound drives one resonator per mode, sample by sample, so the
plate responds to any signal the way the linear theory says: sharply
at its resonances and weakly between them.
The grains are a simplified model. They hop at random and drift down
the slope of the motion wherever the plate’s acceleration exceeds 1
g, and stop where it does not. Where the sand ends up is physical.
How fast it gets there is not calibrated.
Not modelled: the mass of the driver, sand falling off the edge,
air, and the small imperfections that make real plates slightly
asymmetric.