International Applied Mechanics

, Volume 40, Issue 9, pp 1002–1011 | Cite as

Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium

  • V. D. Kubenko
  • V. V. Dzyuba


The paper studies the interaction of a harmonically oscillating spherical body and a thin elastic cylindrical shell filled with a perfect compressible fluid and immersed in an infinite elastic medium. The geometrical center of the sphere is located on the cylinder axis. The acoustic approximation, the theory of thin elastic shells based on the Kirchhoff—Love hypotheses, and the Lamé equations are used to model the motion of the fluid, shell, and medium, respectively. The solution method is based on the possibility of representing partial solutions of the Helmholtz equations written in cylindrical coordinates in terms of partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions at the shell—medium and shell—fluid interfaces and at the spherical surface produces an infinite system of algebraic equations with coefficients in the form of improper integrals of cylindrical functions. This system is solved by the reduction method. The behavior of the hydroelastic system is analyzed against the frequency of forced oscillations.


dynamic interaction elastic shell fluid elastic solid oscillating sphere 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vol’mir, A. S. 1979Shells in Fluid and Gas Flow: Hydroelastic ProblemsNaukaMoscow[in Russian]Google Scholar
  2. 2.
    Guz, A. N., Golovchan, V. T. 1972Diffraction of Elastic Waves in Multiply Connected BodiesNaukova DumkaKiev[in Russian]Google Scholar
  3. 3.
    Guz, A. N., Kubenko, V. D., Cherevko, M. A. 1978Diffraction of Elastic WavesNaukova DumkaKiev[in Russian]Google Scholar
  4. 4.
    V. T. Erofeenko, “Relationship between the basic solutions in cylindrical and spherical coordinates of the Helmholtz and Laplace equations,” Izv. AN BSSR, Ser. Fiz.-Mat. Nauk, No. 4, 42–46 (1982).Google Scholar
  5. 5.
    Kantorovich, L. V., Krylov, V. I. 1962Approximate Methods of Higher AnalysisFizmatgizMoscow—Leningrad[in Russian]Google Scholar
  6. 6.
    Kubenko, V. D. 1987Oscillations of a liquid column in a rigid cylindrical vessel excited by a pulsing spherePrikl. Mekh.23119122Google Scholar
  7. 7.
    Kubenko, V. D. 1986Constructing the potential of a pulsating sphere in an infinite cylindrical cavity filled with an incompressible fluidPrikl. Mekh.22116119Google Scholar
  8. 8.
    V. D. Kubenko, V. V. Gavrilenko, and L. A. Kruk, “Oscillations of an incompressible fluid in an infinite cylindrical cavity containing an oscillating spherical body,” Dokl. AN Ukr., Matem., No. 1, 42–47 (1992).Google Scholar
  9. 9.
    Kubenko, V. D., Gavrilenko, V. V., Kruk, L. A. 1993Constructing the velocity potential for the fluid in an infinite cylindrical cavity containing an oscillating bodyPrikl. Mekh.291925Google Scholar
  10. 10.
    V. D. Kubenko and L. A. Kruk, “An infinite cylindrical shell filled with an incompressible fluid interacting with an oscillating spherical body located on the shell axis,” Dop. AN Ukr., Ser. A, No. 6, 54–58 (1993).Google Scholar
  11. 11.
    Kubenko, V. D., Kruk, L. A. 1994Oscillations of an incompressible fluid in an infinite cylindrical shell containing a spherical body oscillating along the shell axisPrikl. Mekh.303137Google Scholar
  12. 12.
    Morse, P. M., Feshbach, H. 1953Methods of Theoretical PhysicsMcGraw-HillNew YorkGoogle Scholar
  13. 13.
    Shenderov, E. L. 1972Wave Problems in HydroacousticsSudostroenieLeningrad[in Russian]Google Scholar
  14. 14.
    Dzyuba, V. V., Kubenko, V. D. 2002Axisymmetric interaction problem for a sphere pulsating inside an elastic cylindrical shell filled with and immersed into a liquidInt. Appl. Mech.3812101219Google Scholar
  15. 15.
    Kubenko, V. D., Savin, V. A. 2002Dynamics of semi-infinite cylindrical shell with a liquid containing a vibrating spherical segmentInt. Appl. Mech.38974982Google Scholar
  16. 16.
    Kubenko, V. D., Koval’chuk, P. S., Kruk, L. A. 2003On multimode nonlinear vibrations of filled cylindrical shellsInt. Appl. Mech.398592Google Scholar
  17. 17.
    Olsson, S. 1993Point force excitation of an elastic infinite circular cylinder with an embedded spherical cavityJ. Acoust. Soc. Am.9324792488Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • V. D. Kubenko
    • 1
  • V. V. Dzyuba
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKiev

Personalised recommendations