Got curious about the subject just now. This seems to be the only place talking about it, so here are my hints: (I'm just a film major, btw.)
Drumheads, like tuned strings or windpipes, resonate on a fundamental level as well as many harmonic levels above that. The fundamental resonance involves the entire drumhead--a standing half-sine wave can be observed in any diametric cross-section. The first harmonic divides the head into halves, with one diameter having no motion and the diameter perpendicular to that resonating as a sine wave. The next harmonics divide the head into quarters, sixths, and so forth. The harmonics of a drumhead can also extend into concentric subdivisions, where certain rings around the center act as inflections for the standing waves. To further complicate things, the harmonics can be both diametric and concentric, and are often superimposed upon harmonics of other orders.
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This site has some animations of the harmonics in action.)
Even with all this confusion going on, these principles so far apply only to drumheads with stable rims. Striking the rim would introduce different harmonics; so too would shooting the head. And then there's muffling...
If you also want to take the properties of drumsticks into account, I won't object. A considerable amount of force is lost as the rim crushes a small section of the stick, but the elasticity of the wood would help to transfer what energy remains to the tip (and then onto the drumhead). The same would happen for the body of the stick when the tip strikes first. There would be subtle but noticeable variations depending on which (body or tip) struck first and how the energy is distributed.
Keep hunting, guys. (For those of you into muffling, notice how the harmonics don't occur in fifths.

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