Fundamental Frequencies and Critical Circumferential Modes of Fluid-Tank Systems

Abstract eng:
In this work explicit expressions are presented to obtain the fundamental frequency and the circumferential critical n* wave number for the longitudinal critical wave number m=1 for clamped-free vertical cylindrical tanks partially filled with water. The hydrostatic pressure is taken into count, free surface motion is neglected and dynamic pressure is considered like an added virtual mass. The solution is based upon an improved Flügge’s shells theory that is solved by means of the use of covariants and contravariants modals forms. The liquid is assumed as non-viscous and incompressible, and the coupling between the deformable shell and the liquid is taken into count. The solution for the liquid velocity potential satisfies Laplace equation and the relevant boundary condition. A regression model is used in order to fit mathematical results previously computed to obtain two explicit expressions with excellent approximation compared with experimental data. The equations are proposed for the case of steel tanks for a direct use in seismic analysis and design of storage tanks.

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