You know this drum head article makes sense for heads-a thicker head once activated will have longer sustain. More mass vibrating has more momentum to last but with mass it will vibrate at a lower fundamental frequency. You can hear the difference from mass effect on drum shell fundamental in videos whacking it-adding mass lower fundamental (watched Andy do it)-add mass on outer shell and it lowers fundamental more with more mass. But the drum shell thickness it's like opposite- thinner shells have more sustain. and lower tone. You would think increasing thickness like adding mass to a shell would make it have more sustain, once the larger mass in motion, and a lower frequency/pitch fundamental. But that's the sound pitch fundamental of the shell and it's the air sound and then how does thickness influence that final sound.
But It makes sense a thinner shell activates more easily but that mass vibrating should have less sustain and a higher fundamental if a mass effect. A thinner shell will have more internal air volume than a thicker shell so that alone will influence a lower tone. The volume differences has to be stiffness of material. Steel is louder than softer metals, woods are anisotropic so react different than metals. So we have material of same properties (wood) just thickness and it's louder and with slight decrease in air volume so a bit higher fundamental. Now the law of Laplace applies to how forces distributed across wall-so as increase diameter at even given pressure wave the tension/stresses on wall increase. If you increase thickness the stress on wall decreases. How stresses distribute is different-thinner shell force uniform but higher stress but as wall thickens stresses decrease overall but on inner circumference greater than out circumference. A drum shell due to bending straight wood into round should compress inner layer I"d imagine so it naturally has stress-then a smaller diameter from a thicker shell would also put lots more stress on innermost layer- though more mass will increase it's fundamental it should also stiffen and tense the wood making a better funnel for energy transfer and more volume and at higher pitched because difference is air volume.
So now sustain-that has to be how the wood dampens or supports the bouncing air volume within the drum. The drum will be oscillating from strike and pressure wave traveling down an undulating tube to an undulating membrane and that pressure wave will bounce off and go back and forth -so longer more sustain. You could get into all kind of phase interactions but I don't think that's it. Since a thinner wall shell has more sustain-the wave bounces back and forth longer. Now the thinner wall has more air volume for lower pitch but more uniform in stresses and easier to activate so the pressure wave bouncing back and forth probably gets a small push from undulating walls -it acts like a Windkessel. A thicker shell will have more of sound wave energy reach head membrane so little energy loss in shell-its louder. The sound wave likely has less sustain because the energy dissipates bouncing back and forth faster in the stiffer tube. Though a thin shell has smaller mass and momentum for sustain but the stresses are more uniform (and higher stresses than a thinner shell) and the wall more easily excites and vibrate from an air pressure wave and undulating shell must phase to support each other for longer sustain. The thicker shell creates a stiff inner collar more energy goes straight to head-so louder but less undulating for any viscoelastic push. You know even light puts pressure/mechanical force on an object as I recollect.
Then we have different woods in different layers effect-so adding more anisotropic effects to shell. And seems like adding a softer wood to innermost layer is a big deal in effects-lower tone. So that most inside circumferential material does have a big effect and support my idea inner layer stiffness could be explanatory-that thickness increases stress and tension on internal wall to reduce wall movement (although total stress is reduced across wall)-if more wood absorbed sound thicker wouldn't be as loud -but it's louder-so seems the internal stiffness a big deal? The thinner wall takes higher stresses, oscillates easier, so will absorb some of energy going to head to reduce volume but the oscillations must phase with bouncing sound waves to add sustain. Now I claim no authority on this subject as a disclaimer I'm just sharing what I'm reading and how I interpret it.
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