Analytical solution for free vibration of flexible 2D rectangular tanks

This paper provides a brief literature review on dynamic behavior of liquid storage containers. Moreover, the free vibration of two-dimensional deformable rectangular tanks fully-filled with a compressible fluid is analytically investigated, and the exact solutions are derived. In this study, the fluid-structure interaction is rigorously considered, and the fluid is assumed to be irrotational, inviscid and compressible. Furthermore, a closed-form expression is introduced for evaluating the fundamental frequency of the flexible 2D rectangular tanks filled with compressible liquid. In addition, an approximate formula is suggested to determine the corresponding pressure distribution on tank walls. Finally, numerical examples are performed to verify the presented closed-form relations. To study the effect of various parameters on natural frequencies and mode shapes of the fluid-structure system, a sensitivity analysis is also conducted.