Sloshing of liquid in rigid cylindrical container with a rigid annular baffle. Part I: Free vibration

An analytical approach is presented to obtain the sloshing natural frequencies and modes of ideal liquid in a rigid cylindrical container with a rigid annular baffle. The free surface waves of the liquid are considered in the analysis. The artificial interfaces are introduced to divide the complicated liquid domain into several simple sub-domains. The exact analytical solutions of velocity potential of liquid corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The Eigen-frequency equation is precisely derived by using the Fourier-Bessel expansion on the free surface and the artificial interfaces of the liquid. The convergence study shows high accuracy and fast convergence of the present approach. The comparative studies with those available from literature are made, excellent agreements have been achieved. Numerical results showing the variations of natural frequencies and modes versus position and inner diameter of the annular baffle are provided.