Axisymmetric modal analysis of liquid-storage tanks considering compressibility effects

In this paper, we address analytical and numerical studies on the free vibration of uid–structure interaction problems considering the uid compressibility. According to the separation of variables together with the boundary condition enforcement, we rst derive a compressible- uid velocity potential function. Next, we split the structure region into the wet and dry parts, for which we apply the Novozhilov thin shell theory. Combining two dynamic displacement elds, for two split structure parts, using the displacement compatibility conditions, we nally obtain a simultaneous equation system for computing natural frequencies and modes. According to the derived analytical formulae, we compute natural frequencies and modes, stress resultants, together with the comparison with the FEM analysis and the incompressible case. Numerical results show, compared to the incompressible case, that the compressible case produces lower natural frequencies and, furthermore, the relative di erence is in uenced by the slenderness of tanks and the relative liquid ll height