Free vibration analysis of horizontal cylindrical shells including sloshing effect utilizing polar finite elements

• We use the polar finite element for free vibration analysis of the horizontal cylindrical tanks, apparently for the first time.
• We model the sloshing fluid-structure interaction, rigorously.
• We find the coupled natural frequencies instead of the decoupled ones.

The polar finite element is utilized to examine the dynamic characteristics of the horizontal cylindrical shells taking into account sloshing effect. The proposed method is developed by integrating the structural shape functions that are derived on basis of exact solution of equations of motion of shell, the polar finite element and the Sander's thin-walled shell theory. Furthermore, a rigorous fluid-structure interaction analysis is carried out based on the simultaneous solving of the governing equations of the solid and the fluid domains. Moreover, the natural frequencies and the mode shapes of the system are obtained, and the numerical results are compared with available experimental outcomes. By this mean, the accuracy of the presented method is examined thoroughly and it is concluded that the proposed method, in comparisons with other theoretical approaches, is much more accurate under all practical conditions.