> That allows you to model varying wall thickness
That's mentioned in the first chapter of this book [0].
[0] The Finite Element Analysis of Shells – Fundamentals, Chapelle & Bathe
EDIT: I'm aware it is not a surface, but the notion is closer than that of a solid of revolution.
I disagree. Mathematically, I wouldn’t know how to define a solid other than “anything with a volume”.
Certainly, a bell, when defined as a surface of revolution, doesn’t have an interior in a mathematical sense (https://mathworld.wolfram.com/Interior.html), does it?
There’s the convex closure, but that would, for the prototypical bell, add volume ‘outside’ the bell, too.
Also, I think varying wall thickness in bells for centuries was the only known way to tune them. https://en.wikipedia.org/wiki/Pieter_and_François_Hemony#Lif...:
“When struck, a bell produces a number of partials which, if imprecisely tuned, can create an unpleasant sound and which prevents it from harmonizing in accordance with other bells. To address this problem, the Hemony brothers gave their bells a particular profile and thickened it in certain places. The bells were then tuned by hollowing ridges from specific parts of the inner wall until the first few partials were acceptably in tune.”
(Aside: if you want your work to be used for centuries, becoming a professional bell caster seems a good bet)
But surface, by definition, has no concept of thickness, right? Surely there's a better term?
> 'solid' would mean its interior is completely filled.
I think the easiest way to define a bell would be the difference of two solids of revolution (front surface, back surface). What do you call the difference of two solids of revolution?