This article presents an analytical technique for determining the free vibration response of a rectangular tank. It is assumed that this structure has a flexible foundation and rigid walls. The effects of beneath soil are considered by using Winkler and Pasternak foundations. To verify the authors’ responses, the finite element solutions are also compared with the analytical results. Additionally, a closed-form approximate relationship is provided in this research work to determine the first natural frequency of the tank resting on a deformable foundation. In order to find the effect of various parameters, such as the stiffness of the elastic foundation and tank dimensions, on the natural frequencies of this system, a sensitivity analysis is also carried out.

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