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Nonlinear vibration analysis of a partially filled multi-layer cylindrical tank: consideration of the sloshing effects in the fluid–structure interaction

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Abstract

In this work, the nonlinear oscillations of a simply supported, elastic–linear multi-layer circular cylindrical tank, which has been partially filled with liquid, are investigated. The tank materials are elastic, linear, and isotropic; the tank can present one or two layers of materials. The proper law of material distribution is used in the mathematical model to combine the materials, describing the single, or multi-layer, material continuously distributed along the thickness of the tank. The nonlinear equilibrium equation of the tank is described by Donnell’s nonlinear shallow shell theory. An inviscid, irrotational, and incompressible internal fluid is considered in the structural model and the effects of the free surface vibration and its viscous damping are considered. To discretize the nonlinear equilibrium equation of the tank and the fluid–structure interaction, a consistent transverse field displacement, derived from the perturbation technique, is considered and the standard Galerkin method is applied. The numerical results present the influence of the added metallic foam to the cylindrical tank (multi-layer material) and the viscous damping of the fluid’s free surface on the resonance curves, phase portraits, and basins of attraction of the tank. The metallic foam increases the global stiffness of the cylindrical tank, changing the nonlinear behavior of the tank’s resonance curves, while the lower ratio between the viscous damping of the tank and the fluid’s free surface modifies the stability of the nonlinear resonance curves of the tank.

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Acknowledgements

This work was made possible by the support of the Brazilian agencies: CNPq, CAPES, and FAPEG. Ericka L.M.B. Hansen acknowledges the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES), which part-financed her study under Finance Code 001.

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  1. School of Civil and Environmental Engineering, Federal University of Goiás, UFG, Av. Universitária, No. 1488, Setor Universitário, Goiânia, GO, 74605-220, Brazil

    Ericka L. M. B. Hansen & Frederico M. A. Silva

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  1. Ericka L. M. B. Hansen
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Correspondence to Frederico M. A. Silva.

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Hansen, E.L.M.B., Silva, F.M.A. Nonlinear vibration analysis of a partially filled multi-layer cylindrical tank: consideration of the sloshing effects in the fluid–structure interaction. J Braz. Soc. Mech. Sci. Eng. 44, 484 (2022). https://doi.org/10.1007/s40430-022-03800-8

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