Geodesic
On frequencies of free acoustic oscillations in fluid dividing rigid and elastic cylindrical walls of finite length
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 117-123

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The solution of a problem on determination of frequencies and mode shapes of free nonsymmetric oscillations in ring volume filled with ideal compressible fluid is constructed. Internal cylindrical bound and face flat walls are ideally rigid. The thin elastic shell with clamped edges is placed along an external cylindrical boundary. The phenomenon of decreasing of natural frequency at diminution of the thickness of fluid layer is confirmed. 
@article{ZNSL_2002_285_a8,
     author = {Yu. A. Lavrov},
     title = {On frequencies of free acoustic oscillations in fluid dividing rigid and elastic cylindrical walls of finite length},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--123},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a8/}
}
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Yu. A. Lavrov. On frequencies of free acoustic oscillations in fluid dividing rigid and elastic cylindrical walls of finite length. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 117-123. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a8/