Free vibration analysis of liquid storage tanks

To obtain the response of structures subjected to dynamic loading a knowledge of the free vibration characteristics of the structure is essential. The enclosed fluid in the tank exerts inertial loading on the vessel, and part of the fluid may be coupled to the motion of the vessel. for partially filled tanks/shells the free surface motions of the fluid may be coupled with the tank/shell motion, further complicating the analysis. In this paper, variational principles have been used to obtain a functional describing coupled oscillations between a linear elastic body and a liquid of small wave heights. A complementary Rayleigh's quotient has then been introduced to obtain the natural frequencies of circular cylindrical tanks partially filled with liquid and oscillating in an axisymmetric manner.