Investigation of the Acoustic Interaction of Shells with Liquid

We propose a mathematical model of acoustic interaction of the shells of revolution with liquid under axisymmetric loads. The model is based on the linear relations of Timoshenko–Mindlin shells and the acoustic approximation for the liquid. We formulate the initial boundary-value problem and the corresponding variational problem of interaction between two media. For the solution of the variational problem of acoustic interaction between the shell of revolution and the liquid, we develop a projectionmesh scheme, where the Galerkin semidiscretization is used together with approximations of the finiteelement method in the space variables and the one-step recurrence scheme of integration with respect to time. The stress-strain state of the shell subjected to the action of normal hydrostatic pressure is analyzed. The results of numerical analysis of deflections obtained by using the proposed method are compared with the available analytic solutions.

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Correspondence to І. Ye. Bernakevych.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 3, pp. 57–63, July–September, 2015.

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Bernakevych, І.Y., Vahin, P.P., Kozii, І.Y. et al. Investigation of the Acoustic Interaction of Shells with Liquid. J Math Sci 226, 69–78 (2017). https://doi.org/10.1007/s10958-017-3519-9

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