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Stability of an Elastically Supported Cylinder in a Circular Viscous Fluid Flow

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Abstract

A system consisting of two cylinders (the inner cylinder is elastically supported and the outer cylinder is rigidly fixed) and a circulation flow of viscous incompressible fluid between them is considered. In the equilibrium position the cylinders are coaxial and the inner one rotates at a constant angular velocity Ω. An expression is obtained of the force acting on the inner cylinder from the side of the fluid in the approximation of large Reynolds numbers at a small deviation of the inner cylinder from its equilibrium position. It is shown that the force has a hereditary character and depends on the entire trajectory of motion. The stability of the position of the inner elastically supported cylinder is studied in the linear approximation taking into account the hereditary force acting on the inner cylinder.

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REFERENCES

  1. Kapitsa, P.L., Rapidly rotating rotor under friction: stability and whirling speed transition, Zh. Tekh. Fiz., 1939, vol. 9, no. 2. pp. 124–146.

    Google Scholar 

  2. Balandin, D.V., Stabilization of the motion of a rotor in a gas-filled housing, J. Appl. Math. Mech. (Engl. Transl.), 2015, vol. 79, no. 2, pp. 142–147.

  3. Muszynska, A., Whirl and whip - rotor/bearing stability problems, J. Sound. Vib., 1986, vol. 110, no. 3, pp. 443–462.

    Article  ADS  Google Scholar 

  4. Kopiev, V.F., Chernyshev, S.A., and Yudin, M.A., Instability of a cylinder in the circulation flow of incompressible ideal fluid, J. Appl. Math. Mech. (Engl. Transl.), 2017, vol. 81, no. 2, pp. 148–156.

  5. Petrov, A.G. and Yudin, M.A., On the cylinder dynamics in bounded ideal fluid flow with constant vorticity, Fluid Dyn., 2019, vol. 54, no. 7, pp. 898–906.

    Article  Google Scholar 

  6. Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, Oxford: Pergamon Press, 1987.

    Google Scholar 

  7. Petrov, A.G., Hamilton’s principle and certain problems of dynamics of perfect fluid, J. Appl. Math. Mech. (Engl. Transl.), 1983, vol. 47, no. 1, pp. 30–36.

  8. Schlichting, H., Boundary-Layer Theory, New York: McGraw-Hill, 1955.

  9. Petrov, A.G., The force acting on a cylinder in a ring flow of a viscous fluid with a small eccentric displacement, Dokl. Phys., 2018, vol. 63, no. 6, pp. 253–256.

    Article  ADS  Google Scholar 

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Funding

The work is supported by a state task (state registration no. AAAA-A20-120011690138-6).

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. G. Petrov

  2. Zhukovsky Central Aerohydrodynamic Institute, Moscow, Russia

    M. A. Yudin

Authors
  1. A. G. Petrov
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  2. M. A. Yudin
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Correspondence to A. G. Petrov or M. A. Yudin.

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Translated by E. Oborin

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Petrov, A.G., Yudin, M.A. Stability of an Elastically Supported Cylinder in a Circular Viscous Fluid Flow. Fluid Dyn 55, 890–898 (2020). https://doi.org/10.1134/S0015462820070071

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  • DOI: https://doi.org/10.1134/S0015462820070071

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