Skip to main content
SpringerLink
Log in

Coupled seismic vibrations of a pipeline in an infinite elastic medium

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The exact solution of the problem of coupled seismic vibrations of an underground pipeline and an infinite elasticmediumis given. A method dramatically simplifying the solution of the exterior problem for themedium is proposed on the basis of the established theorem on the separation of the boundary conditions for the wave potentials on the surface of the cylinder. The obtained results permit improving the incorrect consideration of the problem accepted in the literature.

The exact statement of the problem allows one to use the solution of the problem as a test for estimating the accuracy of appropriate approaches and solutions in seismodynamics of extended underground structures.

The results of comparison show that the solutions practically coincide both in the subsonic operation mode (when the seismic wave velocity is smaller than the rod velocity of wave propagation in the pipeline) and in the supersonic operation mode, where a resonance is possible. Thus, the high accuracy of the significantly simpler theory of one-dimensional deformation is confirmed.

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. N. M. Newmark, “Problems in Wave Propagation in Soil and Rocks,” in Proc. of the Intern. Symposium on Wave Propagation and Dynamic Properties of Earth Materials, New Mexico, USA (Univ. of New Mexico Press, 1968), pp. 7–26.

    Google Scholar 

  2. A. Sakurai and T. Takahashi, “Dynamic Stress of Underground Pipelines during Earthquakes,” in Proc. of the 4th World Conf. on Earth. Engng (4WCEE), Santiago, Chile, Vol. 2 (1969), pp. 811–895.

    Google Scholar 

  3. A. A. Il’yushin and T. R. Rashidov, “On the Action of SeismicWave on Underground Pipelines,” Izv. Akad. Nauk UzSSR. Ser. Tekhn. Nauk, No. 1, 37–42 (1971); in A. A. Il’yushin, Collected Works, Vol. 4: Modeling of Dynamic Processes in Solids and Engineering Applications (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  4. M. Sh. Israilov, “Seismiodynamics of anUnderground Pipeline,” in Proc. of the 15thWorld. Conf. on Earth. Engng (15WCEE), Lissabon, Portugal (2012), p. 2125.

    Google Scholar 

  5. M. Sh. Israilov, “Seismiodynamics of an Underground Pipeline,” Probl. Mekh. Akad. Nauk RUz, No. 3, 18–24 (2012).

    Google Scholar 

  6. K. Toki and S. Takada, “Earthquake Response Analysis of Underground Tubular Structure,” Bull. Disas. Prev. Res. Inst. Kyoto Univ. 24(2) (221), 107–125 (1974).

    Google Scholar 

  7. M. Sh. Israilov, “Reduction of Boundary Value Problems of Dynamic Elasticity to Scalar Problems forWave Potentials in Curvilinear Coordinates,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 131–136 (2011) [Mech. Solids (Engl. Transl.) 46 (1), 104–108 (2011)].

    Google Scholar 

  8. V. D. Kupradze, Dynamic Problems in Elasticity, in Progress in Solid Mechanics, Vol. 3, Ed. by I. N. Aneddon and R. Hill (North-Holland, Amsterdam, 1963).

    Google Scholar 

  9. M. Sh. Israilov, Dynamic Theory of Elasticity and Wave Diffraction (Izdat. MGU, Moscow, 1992) [in Russian].

    MATH  Google Scholar 

  10. N. N. Lebedev, Special Functions and Their Applications (Fizmatlit, Moscow–Leningrad, 1963) [in Russian].

    Google Scholar 

  11. T. Rashidov, “Differential Equation of Underground Pipeline Vibrations during Earthquakes,” Dokl. Akad. Nauk UzSSR, No. 9, 10–12 (1962).

    Google Scholar 

  12. M. A. Biot, “Propagation of Elastic Waves in a Cylindrical Bore Containing a Fluid,” J. Appl. Phys. 23 (9), 997–1005 (1952); in Collection of Translations “Mechanics”, No. 3 (19), 142–155 (1953).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. M. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill, New York, 1957).

    MATH  Google Scholar 

  14. J. E. White, “ElasticWaves along Cylindrical Bore,” Geophys. 27 (3), 327–333 (1962).

    Article  Google Scholar 

  15. J. E. White, Seismic Waves. Radiation, Transmission, and Attenuation (McGraw-Hill, New York, 1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute of Mathematical Physics and Seismodynamics, Chechen State University, ul. Kievskaya 33, Groznyy, 364037, Russia

    M. Sh. Israilov

Authors
  1. M. Sh. Israilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Sh. Israilov.

Additional information

Original Russian Text © M. Sh. Israilov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 1, pp. 57–66.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Israilov, M.S. Coupled seismic vibrations of a pipeline in an infinite elastic medium. Mech. Solids 51, 46–53 (2016). https://doi.org/10.3103/S0025654416010052

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654416010052

Keywords

Search

Navigation