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Divergence of a helicoidal shell in a pipe with a flowing fluid

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Abstract

This paper considers a solution of the problem of coupled hydroelasticity for a helicoidal shell in a rigid tube with a flowing ideal incompressible fluid, which is of interest for the design of heat exchange systems. The flow is considered potential, and boundary conditions are imposed on the deformed surface. The version of the classical theory of elastic shells as the Lagrangian mechanics of deformable surfaces is used. The longitudinal-torsional vibrations of a long shell and a naturally twisted rod are studied. It is established that the obtained hydrodynamic loads are conservative, so that a divergence type instability is possible. A critical combination of parameters is determined.

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References

  1. W. K. Shchukin, Heat Transfer and Fluid Dynamics of Internal Flows in Fields of Mass Forces [in Russian], Mashinostroenie, Moscow (1970).

    Google Scholar 

  2. A. S. Vol’mir, Shells in Fluid and Gas Flows: Problem of Hydroelasticity [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. H. Ziegler, Principles of Structural Stability, Blaisdell, New York (1971).

    MATH  Google Scholar 

  4. V. V. Eliseev, Mechanics of Elastic Solids [in Russian], St. Petersburg State Polytechnical University, St. Petersburg (2003).

    Google Scholar 

  5. S. A. Bochkarev and V. P. Matvienko, “Numerical modeling of the stability of loaded shells of revolution containing fluid flows,” J. Appl. Mech. Tech. Phys., 49, No. 2, 313–322 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  6. V. V. Eliseev and Y. M. Vetyukov, “Finite deformation of thin shells in the context of analytical mechanics of material surfaces,” Acta Mech., 209, No. 1, 43–57 (2010).

    Article  MATH  Google Scholar 

  7. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions [in Russian], Fizmatlit, Moscow (2003).

    MATH  Google Scholar 

  8. V. P. Il’yin, Methods of Finite Differences and Finite Volumes for Elliptic Equations [in Russian], Institute of Mathematics, Novosibirsk (2000).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State Polytechnical University, St. Petersburg, 195251, Russia

    V. V. Eliseev, Yu. M. Vetyukov & T. V. Zinov’eva

Authors
  1. V. V. Eliseev
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  2. Yu. M. Vetyukov
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  3. T. V. Zinov’eva
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Correspondence to V. V. Eliseev.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 3, pp. 143–152, May–June, 2011.

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Eliseev, V.V., Vetyukov, Y.M. & Zinov’eva, T.V. Divergence of a helicoidal shell in a pipe with a flowing fluid. J Appl Mech Tech Phy 52, 450–458 (2011). https://doi.org/10.1134/S0021894411030151

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  • DOI: https://doi.org/10.1134/S0021894411030151

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