Skip to main content
SpringerLink
Log in

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

  • Published:
International Applied Mechanics Aims and scope

Abstract

A method is proposed to investigate the behavior of an axisymmetric system consisting of an infinite thin elastic cylindrical shell immersed in an infinite elastic medium, filled with a perfect compressible fluid, and containing an oscillating spherical inclusion. The system is subjected to periodic excitation. The task is to detect so-called resonant phenomena, to establish conditions that cause them, and to examine the possibilities of using the characteristic parameters of such a hydroelastic system to influence these conditions. The method allows transforming the general solutions of mathematical physics equations from one coordinate system to another to obtain exact analytic solutions (in the form of Fourier series) to interaction problems for systems of rigid and elastic bodies

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. S. Vol’mir, Shells in a Flow of Fluid and Gas: Problems of Hydroelasticity [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. A. N. Guz and V. T. Golovchan, Diffraction of Elastic Waves by Multiply Connected Bodies [in Russian], Naukova Dumka, Kyiv (1972).

    Google Scholar 

  3. A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kyiv (1978).

    Google Scholar 

  4. V. T. Erofeenko, “Relationship between the fundamental solutions in cylindrical and spherical coordinates of the Helmholtz and Laplace equations,” Izv. AN BSSR, Ser. Fiz.-Mat. Nauk, No. 4, 42–46 (1982).

  5. R. K. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis, Wiley, New York (1964).

    MATH  Google Scholar 

  6. V. D. Kubenko, “Oscillations of a liquid column in a rigid cylindrical vessel excited by a pulsating sphere,” Prikl. Mekh., 23, No. 4, 119–122 (1987).

    Google Scholar 

  7. V. D. Kubenko and V. V Dzyuba, “Dynamic interaction of a rigid cylindrical cavity filled with a compressible fluid with harmonically excited spherical inclusions,” in: Problems of Mechanics (anniversary collection in honor of A. Yu. Ishlinskii’s 90th birthday) [in Russian], Fizmatlit, Moscow (2003), pp. 489–501.

    Google Scholar 

  8. L. M. Lyamshev, “Diffraction of sound by an infinite thin-walled elastic cylindrical shell,” Akust. Zh., 4, No. 2, 31–40 (1958).

    Google Scholar 

  9. L. M. Lyamshev, “Diffraction of sound by a finite thin-walled elastic shell,” DAN SSSR, 115, No. 2, 46–57 (1957).

    Google Scholar 

  10. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 2, McGraw-Hill, New York (1953).

    MATH  Google Scholar 

  11. E. L. Shenderov, Wave Problem in Hydroacoustics [in Russian], Sudostroenie, Leningrad (1972).

    Google Scholar 

  12. E. L. Shenderov, Radiation and Scattering of Sound [in Russian], Sudostroenie, Leningrad (1989).

    Google Scholar 

  13. E. L. Shenderov, “Propagation of a sound wave through an elastic cylindrical shell,” Akust. Zh., 9, No. 2, 32–42 (1963).

    Google Scholar 

  14. N. A. Artsykova, A. K. Pertsev, and S. V. Yakovlev, “Interaction of a spherical shock wave and an elastic circular cylindrical shell,” Int. Appl. Mech., 40, No. 9, 1018–1027 (2004).

    Article  MATH  Google Scholar 

  15. R. D. Doolittle and H. Uberall, “Sound scattering by elastic cylindrical shells,” J. Acoust. Soc. Am., 39, No. 2, 252–257 (1966).

    Article  Google Scholar 

  16. V. V. Dzyuba and V. D. Kubenko, “Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium,” Int. Appl. Mech., 40, No. 9, 1002–1011 (2004).

    Article  MATH  Google Scholar 

  17. A. N. Guz and A. P. Zhuk, “Motion of solid particles in a liquid under the action of an acoustic field: The mechanism of radiation pressure,” Int. Appl. Mech., 40, No. 3, 246–265 (2004).

    Article  MATH  Google Scholar 

  18. P. S. Koval’chuk, “Nonlinear vibrations of a cylindrical shell containing a flowing fluid,” Int. Appl. Mech., 41, No. 4, 405–412 (2005).

    Article  Google Scholar 

  19. P. S. Koval’chuk and L. A. Kruk, “The problem of forced nonlinear vibrations of cylindrical shells completely filled with liquid,” Int. Appl. Mech., 41, No. 2, 154–160 (2005).

    Article  Google Scholar 

  20. 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).

    Article  MATH  Google Scholar 

  21. 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).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv

    V. D. Kubenko & V. V. Dzyuba

Authors
  1. V. D. Kubenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Dzyuba
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 82–97, July 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kubenko, V.D., Dzyuba, V.V. Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium. Int Appl Mech 42, 797–809 (2006). https://doi.org/10.1007/s10778-006-0148-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-006-0148-2

Keywords

Search

Navigation