The exact solution to the free vibration problem of circular cylindrical shells half-filled with liquid and with the shell axis orthogonal to the gravitational field is analytically obtained and approximate models are proposed to estimate natural frequencies and mode shapes of partially filled shells. In the problem considered, the free surface of the liquid is parallel to the shell axis with lack of axisymmetry of the liquid-shell system. The shell is considered to be simply supported at both ends. The kinetic energy of the system is analytically evaluated for an inviscid and incompressible liquid. Natural frequencies and mode shapes are found by using a Galerkin equation obtained by minimizing the Rayleigh quotient. The study is based on the development of the radial displacement in a Fourier series and it is independent of the shell theory. Numerical data are presented for both eigenvalues and eigenvectors. The curves of natural frequencies as functions of the water level in the shell are shown. The theoretical study is validated through comparison with results of experimental modal analyses performed on a AISI 304 stainless steel pipe supported by two thin diaphragms and filled with water to different levels.
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