Natural Modes of Liquid Sloshing in a Cylindrical Container with an Elastic Cover

•The coupled vibration of fluid and plate cover is investigated in an upright circular tank with different plate edge conditions.•Two efficient solution methods have been developed and proved to be equivalent.•A simple form of equation has been obtained for natural frequencies.•Natural mode shapes are investigated.•The distribution of the maximum principal strain is analysed for the elastic cover. Liquid sloshing and its interaction with an elastic cover in a cylindrical tank is considered. The velocity potential for the fluid flow is expanded into the Bessel-Fourier series as commonly used. An efficient scheme is then developed, which allows the plate deflection to use the same type of expansion as the potential. When these two series are matched on the interface of the fluid and the plate, together with the edge conditions, the unknown coefficients in the two expansions can be easily obtained. This is much more convenient than the common procedure where a different expansion is used for the plate and upon matching each term in the series of the plate is further expanded into the series used for the potential. Through the developed method, an explicit equation is derived for the natural frequencies and extensive results are provided. The corresponding natural mode shapes and principal strains distribution of the elastic cover are also investigated. Results are provided and the underlining physics is discussed. To verify the obtained results, the problem is also solved through a different method in which the potential is first expanded into vertical modes. Another explicit equation for the natural frequencies is derived. While the equation may be in a very different form, through the residual theorem, it is found that the second equation is identical to the first one.