Abstract
An interaction problem is formulated for a spherical body oscillating in a prescribed manner inside a thin elastic cylindrical shell filled with a perfect compressible liquid and submerged in a dissimilar infinite perfect compressible liquid. The geometrical center of the sphere is on the cylinder axis. The solution is based on the possibility of representing the partial solutions of the Helmholtz equations written in cylindrical coordinates for both media in terms of the partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions on the sphere and shell surfaces results in an infinite system of linear algebraic equations. This system is used to determine the coefficients of the Fourier-series expansions of the velocity potentials in terms of Legendre polynomials. The hydrodynamic characteristics of both liquids and the shell deflections are determined. The results obtained are compared with those for a sphere oscillating on the axis of an elastic cylindrical shell filled with a compressible liquid (the ambient medium being neglected).
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REFERENCES
A. S. Vol'mir, Shells in a Fluid Flow. Hydroelastic Problems [in Russian], Nauka, Moscow (1979).
A. N. Guz and V. T. Golovchan, Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kiev (1972).
A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev (1978).
V. T. Erofeenko, “Relation between the basic solutions of the Helmholtz and Laplace equations in cylindrical and spherical coordinates,” Izv. AN BSSR, Ser. Fiz.-Mat. Nauk, No. 4, 42–46 (1982).
E. A. Ivanov, Diffraction of Electromagnetic Waves by Two Bodies [in Russian], Nauka Tekhn., Minsk (1968).
L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow-Leningrad (1962).
V. D. Kubenko, “Oscillation of a liquid column in a rigid cylindrical vessel excited by a pulsating sphere,” Prikl. Mekh., 23, No. 4, 119–122 (1987).
V. D. Kubenko, “On constructing the potential of a pulsating sphere in an infinite cylindrical cavity filled with an incompressible liquid,” Prikl. Mekh., 22, No. 7, 116–119 (1986).
V. D. Kubenko, V. V. Gavrilenko, and L. A. Kruk, “Oscillations of an incompressible liquid in an infinite cylindrical cavity with a pulsating spherical body inside,” Dokl. AN Ukrainy, Ser. Mat., No. 1, 42–47 (1992).
V. D. Kubenko, V. V. Gavrilenko, and L. A. Kruk, “Constructing the velocity potential of a liquid in an infinite cylindrical cavity containing a pulsating body,” Prikl. Mekh., 29, No. 1, 19–25 (1993).
V. D. Kubenko and L. A. Kruk, “Interaction of an infinite cylindrical shell filled with a liquid and a spherical body pulsating on the shell axis,” Dop. AN Ukrainy, Ser. A, No. 6, 54–58 (1993).
V. D. Kubenko and L. A. Kruk, “On the oscillations of an incompressible liquid in an infinite cylindrical shell containing a spherical body oscillating along the shell axis,” Prikl. Mekh., 30, No. 4, 31–37 (1994).
E. L. Shenderov, Wave Problems of Hydroacoustics [in Russian], Sudostroenie, Leningrad (1972).
V. D. Kubenko and V. V. Dzyuba, “Interaction between an oscillating sphere and a thin elastic cylindrical shell filled with a compressible liquid. Internal axisymmetric problem,” Int. Appl. Mech., 37, No. 2, 222–230 (2001).
V. D. Kubenko and V. V. Dzyuba, “The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law,” Int. Appl. Mech., 36, No. 6, 779–788 (2000).
V. D. Kubenko and L. A. Kruk, “Pulsating liquid flow past a spherical body in an infinite cylinder,” Int. Appl. Mech., 35, No. 6, 555–560 (1999).
S. Olsson, “Point force excitation of an elastic infinite circular cylinder with an embedded spherical cavity,” J. Acoust. Soc. Am., 93, No. 5, 2479–2488 (1993).
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Dzyuba, V.V., Kubenko, V.D. Axisymmetric Interaction Problem for a Sphere Pulsating Inside an Elastic Cylindrical Shell Filled with and Immersed Into a Liquid. International Applied Mechanics 38, 1210–1219 (2002). https://doi.org/10.1023/A:1022206328763
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DOI: https://doi.org/10.1023/A:1022206328763