The British inventor Marcus de Mowbray makes drums that are basically frames with a top and a bottom rim and head but with no shell in between n and they still sound remarkably like other drums. The diameter of the head and the distance between the top and bottom head seems to be enough to do the trick. Marcus also makes timpani with just a top head and no massive copper bowl. And they sound like timpani. Other drums, like Arbiter’s Flats and Remo’s Roto-toms, which have just top heads but no shells, also project loads of sound.
The sound, though, is more open and spread-out, which is perhaps what you’d expect. When it comes to normal, wood shelled drums, the size of drum, how it’s tuned and played and the type of head all have a bigger impact on the perceived sound than the shell itself. What the shell does though is to change the timbre slightly n it’s the icing on the cake for the high budget buyer. If you want proof that the shell affects the sound you only have to think of the difference in timbre between a steel shell and a wood shell snare drum.
Most drummers can hear such a difference very easily, though they might not always recognize it on a recording. Obviously the shell acts as a resonating chamber absorbing and reflecting, reducing and amplifying various frequencies n acting like a combination of amplifier and graphic equalizer n and so the sound is colored and altered in subtle ways. But never forget that the generating source is the head.