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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Druckformat: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v32.i2.50
pages 199-213

An Interior Axisymmetric Problem of Interaction Between a Thin Elastic Cylindrical Shell, Filled with a Compressible Fluid and Immersed in an Infinite Compressible Fluid, and an Oscillating Sphere

V. V. Dzyuba
S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. D. Kubenko
S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine


The paper states a problem of interaction between an oscillating spherical body and a thin elastic cylindrical shell, filled with ideal compressible liquid and submerged into an infinite ideal compressible medium with different properties. The geometrical center of the sphere is located on the cylinder's axis. Development of the solution is based on a possibility to represent particular solutions of the Helmholtz equations, written for both media in the cylindrical coordinates, by means of particular solutions in spherical coordinates and vice versa. By satisfying boundary conditions on the surfaces of the sphere and the shell, an infinite system of linear algebraic equations is produced to determine the coefficients in the Fourier expansion of the liquid's velocity potential with respect to the Legendre polynomials. Hydrodynamic properties of the fluids filling the cylindrical shell and surrounding it are determined, as well as flexural deformations of the cylindrical shell. A comparison is made with a sphere vibrating on the axis of a thin elastic cylindrical shell filled with a compressible fluid (not taking the exterior fluid into account).

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