Free vibration of cylinders containing liquid

Series of displacement functions for three-dimensional motion are assumed for a cantilevered circular cylindrical shell. The classical Rayleigh-Ritz method is used to obtain a set of equations describing the behavior of the vibrating shell. Solution of the system reduces to a standard eigenvalues problem. Computer solutions give numerical results for natural frequencies. Some mode shapes are illustrated. A potential function is developed for a liquid contained in the shell. Its coefficients insure compatibility of the shell-liquid interface. The liquid kinetic energy is computed and added to that of the shell. Resulting natural frequencies are compared with some experimental data.

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