Liquid sloshing in rigid cylindrical container with multiple rigid annular baffles: Free vibration

A semi-analytical approach is presented to obtain the natural frequencies and vibration modes of ideal liquid sloshing in a rigid partially liquid-filled cylindrical container with multiple rigid annular baffles of the same inner radius. The complicated liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain is of class C1 with continuity boundary conditions. Based on the superposition principle, the analytical solutions of the liquid velocity potential corresponding to each liquid sub-domain are obtained by means of the method of separation of variables. The eigenfrequency equation is obtained by expanding the free surface condition and the artificial interface conditions into the Fourier series in the liquid height direction and the Bessel series in the radial direction. Stable and fast numerical computations are observed by the convergence study. Excellent agreements have been achieved in the comparison of results obtained by the proposed approach with those given by finite element software ADINA. The natural frequencies and mode shapes versus the position, the inner radius and the number of the annular baffles are discussed in detail.