Free Vibrations of Fluid-Filled Cylindrical Shells

The mode shapes and frequencies of free vibration of cantilevered cylindrical shells, partially or completely filled with fluid, are of use in the analysis of the response of such shells to a transient excitation. The kinetic energy of the fluid filling in each mode of vibration is evaluated and frequency determinants are presented for the computation of both the frequencies and the mode shapes of the partially filled shells. The results may be applied to problems such as the response of fuel storage tanks to earthquake or blast loadings. The frequencies and mode shapes of free vibrations of thin, empty, cylindrical shells, free at the top and simply supported at the base, have been studied previously. The present paper extends the application of these modes to the case of shells that are partially filled with a fluid by using the mode shapes of the empty shells as generalized coordinates for the shell-fluid interaction problem. The kinetic energy of the fluid is evaluated in each mode, assuming that the fluid motion is both irrotational and incompressible. Expressions for the displacements of the free fluid surface are also presented. Numerical virtual mass and fluid surface coefficients are presented as a function of the height of the fluid in a tank with a height-to-radius ratio of 0.8.