Abstract
This paper presents a study of small, steady free oscillations of a system consisting of an elastic shell filled with an ideal incompressible fluid. To describe the motion of the shell differential equations of the momentless [membrane] theory are used. The applicability of this theory for computing of frequencies which are not too high and of the modes of oscillation was already established in [1], The motion of the fluid is taken as potential one. Exact solutions of the problems of free oscillations for the following types of shell fully filled with fluid were obtained: a cylindrical shell with one or two rigid ends, a closed spherical, and a half-spherical one.
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