Skip to main content
SpringerLink
Log in

Stability analysis of loaded coaxial cylindrical shells with internal fluid flow

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

We present numerical results for dynamical stability of loaded coaxial shells of revolution interacting with the internal fluid flow. The motion of the incompressible fluid is described in the framework of the theory of frictionless potential flow, whereas the static load acting on the shells is caused by the steady forces of viscous drag arising in the viscous turbulent flow in a closed channel. For shells with different boundary conditions, we study how the stability boundary is affected by the value of the gap between the shells for different versions of the outer shell rigidity and fluid flow. We show that, as in the case of unloaded coaxial shells, there is a significant deviation from the previous numerical and analytical results.

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. M. P. Païdoussis, S. P. Chan, and A. K. Mirsa, “Dynamics and Stability of Coaxial Cylindrical Shells Containing Flowing Fluid,” J. Sound Vibr. 97(2), 201–235 (1984).

    Article  ADS  Google Scholar 

  2. M. P. Païdoussis, V. B. Nguyen, and A. K. Mirsa, “A Theoretical Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid,” J. Fluids Struct. 5(2), 127–164 (1991).

    Article  ADS  Google Scholar 

  3. M. P. Païdoussis, A. K. Mirsa, and S. P. Chan, “Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid,” ASME J. Appl. Mech. 52(2), 389–396 (1985).

    Article  ADS  Google Scholar 

  4. M. P. Païdoussis, A. K. Mirsa, and V. B. Nguyen, “Internal- and Annular-Flow-Induced Instabilities of a Clamped-Clamped or Cantilevered Cylindrical Shell in a Coaxial Conduit: The Effects of System Parameters,” J. Sound Vibr. 159(2), 193–205 (1992).

    Article  ADS  MATH  Google Scholar 

  5. V. B. Nguyen, M. P. Païdoussis, and A. K. Mirsa, “A CFD-Based Model for the Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Viscous Fluid,” J. Sound Vibr. 176(1), 105–125 (1994).

    Article  ADS  MATH  Google Scholar 

  6. A. El. Chebair, M. P. Païdoussis, and A. K. Mirsa, “Experimental Study of Annular-Flow-Induced Instabilities of Cylindrical Shells,” J. Fluids Struct. 3(4), 349–364 (1989).

    Article  Google Scholar 

  7. V. B. Nguyen, M. P. Païdoussis, and A. K. Mirsa, “An Experimental Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid,” J. Fluids Struct. 7(8), 913–930 (1993).

    Article  ADS  Google Scholar 

  8. M. Amabili and R. Garziera, “Vibrations of Circular Cylindrical Shells with Nonuniform Constraints, Elastic Bed, and Added Mass; Part III: Steady Viscous Effects on Shells Conveying Fluid,” J. Fluids Struct. 16(6), 795–809 (2002).

    Article  ADS  Google Scholar 

  9. S. A. Bochkarev and V. P. Matveenko, “Numerical Simulation of Dynamical Behavior of Coaxial Cylindrical Shells Conveying Fluid,” in Proc. XVI Winter School in Continuum Mechanics (Continuum Mechanics as Foundation of Modern Technologies), CD (Perm, IMSS UrO RAN, 2009) [in Russian].

    Google Scholar 

  10. V. L. Biderman,Mechanics of Thin-Walled Structures (Mashinostroenie, Moscow, 1977) [in Russian].

    Google Scholar 

  11. S. A. Bochkarev and V. P. Matveenko, “Numerical Modelling of the Stability of Loaded Shells of Revolution Containing Fluid Flows,” Zh. Prikl. Mekh. Tekhn. Fiz. 49(2), 185–195 (2008) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 49 (2), 313–322 (2008)].

    MathSciNet  Google Scholar 

  12. A. S. Vol’mir, Shells in Fluid Flow. Problems of Hydroelasticity (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  13. C. A. J. Fletcher, Computational Galerkin Methods (Springer, New York-Berlin, 1984; Mir, Moscow, 1988).

    MATH  Google Scholar 

  14. S. A. Bochkarev and V. P. Matveenko, “Numerical Study of the Influence of Boundary Conditions on the Dynamic Behavior of a Cylindrical Shell Conveying a Fluid,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 189–199 (2008) [Mech. Solids (Engl. Transl.) 43 (3), 477–486 (2008)].

  15. I. Michiyoshi and T. Nakajima, “Fully Developed Turbulent Flow in a Concentric Annulus,” J. Nuclear Sci. Tech. 5(7), 354–359 (1968).

    Article  Google Scholar 

  16. V. P. Matveenko, “On an Algorithm for Solving the Problem of Natural Vibrations of Elastic Bodies by Finite Element Method,” in Boundary-Value Problems of Elasticity and Viscoelasticity (Ural Sci. Center, USSR Akad. Sci., Sverdlovsk, 1980), pp. 20–24 [in Russian].

    Google Scholar 

  17. A. George and J. W.-H. Liu, Computer Solution of Large Sparse Positive Definite Systems (Prentice-Hall, Englewood Cliffs, New Jersey, 1981; Mir, Moscow, 1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Akad. Koroleva 1, Perm, 614013, Russia

    S. A. Bochkarev & V. P. Matveenko

Authors
  1. S. A. Bochkarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Matveenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Bochkarev.

Additional information

Original Russian Text © S.A. Bochkarev, V.P. Matveenko, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 6, pp. 29–45.

About this article

Cite this article

Bochkarev, S.A., Matveenko, V.P. Stability analysis of loaded coaxial cylindrical shells with internal fluid flow. Mech. Solids 45, 789–802 (2010). https://doi.org/10.3103/S002565441006004X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S002565441006004X

Keywords

Search

Navigation