Abstract
The dynamic behavior of cylindrical tanks in the empty or water-filled condition is analyzed. The equation of free vibration is derived for tanks fixed at the base and free at the top by using Lagrange’s equation in which the various energy expressions are worked out on the basis of assumed beam-type functions for the displacements of the shell. Equations are finally derived for natural time periods, mode shapes, and the virtual mass factor of water which may be used for obtaining the response of the tank to superimposed dynamic forces. The effects of length-radius ratio and varying water depth on the natural frequencies are studied by numerical examples.
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