Axisymmetrical Vibrations, of Tanks—Analytical

Abstract

An analytical method for the computation of the axisymmetrical dynamic characteristics of partly‐filled cylindrical tanks is presented. The liquid is assumed to be inviscid and incompressible. The tank shell is assumed to be of constant thickness and its material to be linearly elastic. Under these assumptions, two coupled partial differential equations govern the vibrations of the shell. Because the tank is partly‐filled with liquid, two different solutions are obtained for the lower (wet) and upper (dry) portions of the shell. A system of linear homogeneous algebraic equations is obtained by satisfying the boundary conditions at the bottom and top of the tank and the compatibility equations at the junction of the wet and dry parts of the shell. The determinant of coefficients of this system leads to the frequency equation. The natural frequencies, mode shapes and stress distributions showed excellent agreement with those obtained from a numerical solution.