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A Study of Stability of Rotation for Rotary Systems with Liquid

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Abstract

We propose a new method for studying stability which, in contrast to the traditional D-decomposition method, does not require knowledge of the characteristic equation. The method is effective in a wide class of problems in the dynamics of bodies with cavities containing a liquid.

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References

  1. Gantmakher, F. R. Teoriya matrits (Theory of Matrices). (Nauka, Moscow, 1967).

    MATH  Google Scholar 

  2. Neimark, Yu. I. Ustoichivost’ linearizovannykh sistem (Stability of Linearized Systems). (LKVVIA, Leningrad, 1949).

    Google Scholar 

  3. Derendyaev, N. V. & Sandalov, V. M. On the Stability of Stationary Rotation of a Cylinder Partially Filled with Viscous Incompressible Liquid. Prikl. Mat. Mekh 46(no. 4), 578–586 (1982).

    Google Scholar 

  4. Derendyaev, N. V. & Senyatkin, V. A. Stability Conditions for the Stationary Rotation of a Cylinder Filled with Stratified Nonhomogeneous Viscous Incompressible Liquid. Prikl. Mekh. Theor. Fiz no. 1, 34–44 (1984).

    Google Scholar 

  5. Watson, G.N.A Treatise on the Theory of Bessel Functions, Cambridge: Cambridge Univ. Press, 1944. Translated under the title Teoriya besselevykh funktsii, Moscow: Inostrannaya Literatura, 1949.

  6. Bolotin, V. V. Nekonservativnye zadachi teorii uprugoi ustoichivosti (Nonconservative Problems of Elastic Stability Theory). (Fizmatgiz, Moscow, 1961).

    Google Scholar 

  7. Derendyaev, N. V. & Sandalov, V. M. Stability of Stationary Rotation of a Rotor Filled with Stratified Viscous Incompressible Liquid. Mashinovedenie no. 1, 19–26 (1986).

    Google Scholar 

  8. Sandalov, V.M., Dinamicheskaya neustoichivost’ turbomashin, obuslovlennaya radialanymi zazorami v podshipnikakh skolazheniya i zhidkostnym napolneniem polostei rotorov (Dynamic Instability of Turbo Machines Caused by Radial Gapes in Friction Bearings and Hydraulic Fluid in Rotor Pockets), Cand. Sci. Dissertation, Gorky, 1983.

  9. Senyatkin, V.A.Neustoichivost’ rotornykh sistem, obuslovlennaya soderzhashcheisya v nikh vyazkoi zhidkost’yu (Instability of Rotor Systems Caused by Viscous Liquid Contained in Them), Cand. Sci. Dissertation, Gorky, 1985.

  10. Soldatov, I.N. Ustoichivost’ i avtokolebaniya rotornykh sistem, soderzhashchikh provodyashchuyu vyazkuyu zhidkost’ v magnitnom pole (Stability and Autooscillations of Rotor Systems Containing Conductive Viscous Liquid in a Magnetic Field), Cand. Sci. Dissertation, Nizhny Novgorod, 1994.

  11. Derendyaev, N. V., Vostrukhov, A. V. & Soldatov, I. N. Stability and Andronov-Hopf Bifurcation of Steady-State Motion of Rotor System Partly Filled with Liquid: Continuous and Discrete Models. ASME. J. Appl. Mech. 73(no. 4), 580–589 (2006).

    Article  Google Scholar 

  12. Derendyaev, N. V. Ustoichivost’ vrashcheniya rotornykh sistem, soderzhashchikh zhidkost’ (Rotation Stability for Rotor Systems Containing Liquid). (Nizhegorodsk. Gos. Univ, Nizhny Novgorod, 2014).

    Google Scholar 

  13. Derendyaev, N. V., Sandalov, V. M. & Soldatov, I. N. On the Birth of a Periodic Motion in the Stability Problem for Stationary Rotation of a Vertical Rotor on Fluid Dynamic Bearings. Mashinovedenie no. 4, 98–103 (1988).

    Google Scholar 

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Acknowledgements

We are grateful to D.N. Derendyaev for help in writing the paper.

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Derendyaev, N. A Study of Stability of Rotation for Rotary Systems with Liquid. Autom Remote Control 81, 1450–1460 (2020). https://doi.org/10.1134/S000511792008007X

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