Free vibration analysis of cylindrical tanks partially filled with liquid

A simple but effective modal solution based on the underlying ideas of the hierarchical finite element method is presented for evaluating the free vibration characteristics of vertical, thin, circular cylindrical shells, partially or completely filled with liquid and subjected to any variationally consistent set of boundary conditions on the lower and upper boundaries. Effects of static liquid pressure, in-plane inertias and liquid free surface motions are taken into account. The solution of the shell problem is obtained through a procedure in which Sanders' shell equations are transformed into a new system of first order ordinary differential equations which are solved by the Galerkin error-minimization procedure. The system variables are those quantities which appear in the boundary conditions on a rotationally symmetric edge of a cylindrical shell. The liquid is taken as non-viscous and incompressible, and the coupling between the deformable shell and this medium is taken into account. The solution for the liquid velocity potential is assumed as a sum of two sets of linear combinations of suitable harmonic functions which satisfy Laplace equation and the relevant boundary conditions. This procedure leads to a determinantal equation for the determination of the shell and liquid natural frequencies and the associated mode shapes. Application of the method to a few selected cases and comparisons of the numerical results with those obtained by other theories and from experiments are found to be good and demonstrate the effectiveness and accuracy of the present methodology. (C) 1996 Academic Press Limited