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Nonlinear Equations of Motion of an Extensible Underground Pipeline: Derivation and Numerical Modeling

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Abstract

Slow motion of a pipeline modeled by a bent rod in a viscous medium is studied. It is assumed that the displacements of the axial line of the rod are finite and its strains are small. The mutual influence of the tensile axial force and transverse deflections is taken into account. Equations of motion are derived and some numerical examples are considered. An approximate estimate of stresses in the pipeline wall is given.

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REFERENCES

  1. L. N. Kartvelishvili, “Water hammer: Fundamentals and state of the art of the theory,” Gidrotekh. Str., No. 9, 49–54 (1994).

    Google Scholar 

  2. B. N. Klochkov and E. A. Kuznetsova, “Nonlinear variations in the shape of an elastic pipe with an internal fluid flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4, 46–55 (2000).

    Google Scholar 

  3. D. G. Lynch, S. L. Waters, and T. J. Pedley, “Flow in a tube with non-uniform, time-dependent curvature: governing equations and simple examples,” J. Fluid Mech., 323, 237–265 (1996).

    Google Scholar 

  4. U. Lee, C. H. Pak, and S. C. Hong, “The dynamics of a piping system with internal unsteady flow,” J. Sound Vibr., 180, No. 2, 297–311 (1995).

    Google Scholar 

  5. S. A. Berger, L. Talbot, and L. S. Yao, “Flow in curved pipes,” Annu. Rev. Fluid Mech., 15, 461–512 (1983).

    Google Scholar 

  6. V. A. Rukavishnikov and O. P. Tkachenko, “Numerical and asymptotic solution of equations of propagation of hydroelastic vibrations in a curved pipe,” J. Appl. Mech. Tech. Phys., 41, No. 6, 1102–1110 (2000).

    Google Scholar 

  7. S. P. Timoshenko, “Buckling of shallow bars and slightly curved plates,” in: Stability of Bars, Plates, and Shells [in Russian], Nauka, Moscow (1971), pp. 662–669.

    Google Scholar 

  8. A. S. Vol’mir, Stability of Elastic Systems [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  9. N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydromechanics [in Russian], Vol. 2, Gostekhteoretizdat, Moscow (1948).

    Google Scholar 

  10. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970).

    Google Scholar 

  11. G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Handbook on Strength of Materials [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

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Authors and Affiliations

  1. Computation Center, Far-East Division, Russian Academy of Sciences, Khabarovsk, 680021

    V. A. Rukavishnikov & O. P. Tkachenko

Authors
  1. V. A. Rukavishnikov
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  2. O. P. Tkachenko
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Rukavishnikov, V.A., Tkachenko, O.P. Nonlinear Equations of Motion of an Extensible Underground Pipeline: Derivation and Numerical Modeling. Journal of Applied Mechanics and Technical Physics 44, 571–583 (2003). https://doi.org/10.1023/A:1024213527532

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  • DOI: https://doi.org/10.1023/A:1024213527532

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