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Free hydroelastic coupled vibration analysis of frictionless liquids with a free surface in spherical tanks with a flexible bottom has been performed. The side wall has been considered to treate as a rigid body. The flexible bottom treats as a membrane at a certain distance bellow the center point, and the free surface is considered as a cross cutting at the top of the center point. The spherical coordinate system is adopted to derive the governing coupled equations, and finally a vibration analysis is carried out, using the traditional Galerkin's method, leading to closed-form solutions. Effects of various system parameters, i.e., membrane tension, liquid density, geometric parameters of the system such as the container radius, free surface distance discriminate parameter, and bottom distance discriminate parameter on the vibration behavior are investigated. The novelty of the present work is to obtain direct formulas for hydroelastic coupled vibration analysis of the mentioned system, which can be easily used in engineering design applications. Coupling between two mode numbers can be clearly seen in results, in other words, there is a coupling between vibration modes as interaction in spherical geometry.

Keywords: Hydroelastic coupled vibration, spherical container, membrane bottom, liquid free surface

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