You might be able to use the drum as a Chladni plate, by attaching a speaker to the bottom side and playing sine waves through it. See here:
https://sciencedemonstrations.fas.harvard.edu/presentations/chladni-plates
I'm not sure how well this would work for a drum in practice but the principle is there. I have difficulty seeing how else you would be able to demonstrate the vibrational modes of the drum.
I'm not sure what your physics background is so here's the gist. The drum will have a number of resonant frequencies ##\omega_i##, each of which is associated with
one or more of the oscillation 'modes' which are pictured in the image shown by anorlunda. Here's an interactive demonstration of what the oscillations modes like:
https://demonstrations.wolfram.com/NormalModesOfACircularDrumHead/
Fortunately in the case of a drum it's a very concrete demonstration. The plot is showing the skin of the drum, displaced up or down, although this displacement is greatly exaggerated compared to a real drum. An arbitrary vibration of a drum skin is modeled as a
linear combination of these vibrational patterns.
If you play a tone through the speaker at the bottom of a chladni plate (or a drum) at a frequency that matches one or more of the oscillation modes, $\omega_i$, then the drum will naturally vibrate in response with some linear combination of all the modes that have that specific frequency. You can see in the linked demonstration that the vibrational modes are indexed by ##n## and ##k##. If you take care to vibrate the drum right at its center, then (hopefully) all the modes with ##n\neq 0## will not be stimulated. Only the modes with rotational symmetry, like the first and fourth modes in the image shown by anorlunda.
Each of the modes with ##n = 0## has different frequencies, so it should be possible to stimulate one at a time. This is what you want, because then you can see the parts of the drum skin that 'nodes' which remain fixed and do not oscillate up and down. If you just hit the drum, you would get a linear combination of modes and no particular points on the drum skin would be stationary except the outer rim. When you cause the drum to oscillate in a single mode, particles on the drum (e.g. fine sand, maybe styrofoam?) will take something of a random walk on the drum due to the agitation back and forth as the drum skin flaps up and down. However those particles that randomly make it to one of the still spots in the drum skin will stay there undisturbed. This may also be due to static friction which keeps particles hugging the skin until the skin 'falls' underneath them, causing them to actively seek out nodal points. I'm not sure.
In any case, the point is that if you put a speaker under the drum right at the center, place fine sand on the drum with good contrast, and scan through a range of sine wave frequencies, you ought to be able to observe this effect of the sand collecting in the nodal points of the oscillatory mode. You could demonstrate the different vibrational modes by scanning through the frequencies finding the higher-frequency modes.
