The shell is made of metal, the inside and exterior are inviscid fluids.
The ratio of shell thickness to radius (h/a) ranges from 0.5 % to 2 %.
I have written Fortran programs for the models described in the papers listed below but they are all unsatisfactory in some respect. Hickling used full exact elasticity, but there seem to be misprints in the paper. The others are thin-shell models and yield a resonance frequency of zero at particular values of h/a. I will give further details to anyone who asks and is acquainted with the issue.
Hickling 1964
Lou & Su 1978
Felippa & Geers 1980 (same result as preceding paper)
Dean & Werby 1992