V.V.Dzyuba, V.D.Kubenko Internal axisymmetric problem on interaction of thin elastic cylindrical shell, filled with a compressible liquid and immersed into an infinite compressible liquid, and having an oscillating sphere |
Acoustic bulletin, Vol. 5 ¹ 2, (2002) |
| The problem on interaction between an oscillating spherical body and a thin elastic cylindrical shell filled by an ideal compressible liquid and submerged into an infinite ideal compressible medium with other parameters is formulated. Geometrical center of the sphere is located on the cylinder's axis. Development of the solution is based on the 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. After satisfying boundary conditions on the surfaces of the sphere and the shell, the infinite system of linear algebraic equations is obtained to determine the coefficients in the Fourier expansion of the liquid's velocity potential with respect to the Legendre polynomials. Hydrodynamic characteristics of liquids filling the cylindrical shell and surrounding it are determined, as well as flexural deformations of the cylindrical shell. A comparison with the sphere vibrating at the axis of a thin elastic cylindrical shell filled by the compressible liquid (not accounting to the external liquid) is made. |
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KEY WORDS: thin-walled shell, compressible fluid, oscillations, spherical body, velocity potential |
| TEXT LANGUAGE: Russian |