Closed cylindrical shell in a supersonic gas flow in the presence of a non-uniform temperature field

System analysis, control and data processing


Baghdasaryan G. Y.1*, Mikilyan M. A.1**, Vardanyan I. A.1***, Panteleyev A. V.2****

1. Russian-Armenian University, 123, Hovsep Emin str., Yerevan, 0051, Armenia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The article considers the problem of stability of a closed cylindrical shell under the action of an inhomogeneous temperature field and a supersonic gas flow, flowing around the shell. The authors obtained stability conditions for the unperturbed state of the aerothermoelastic system under consideration. It is shown, that the combined action of the temperature field and the ambient flow can control the process of stability, and change significantly the value of the flutter critical velocity by means of the temperature field.

The study is based on the following well-known assumptions:

a) Kirchhoff-Love's hypothesis on undeformable normals;

b) “The law of flat sections” in determining the aerodynamic pressure;

c) The linear law of temperature variation over the thickness of the shell;

d) The Neumann hypothesis on the absence of the temperature changes.

For simplicity and clarity, it is assumed that the heat exchange with the environment from the shell front surfaces proceeds according to the Newton – Richman law (the temperature remains constant on the surfaces), and the side surfaces are thermally insulated.

Under the action of a stationary temperature field, non-uniform in thickness, the shell bulges (with deflection and longitudinal movement) and, as a result, the aeroelastic pressure occurs. The above said bulging state is presumed unperturbed, and its stability is being studied under the action of the temperature field and the pressure of the flowing gas flow. Stability regions are plotted, and the the critical velocity values are obtained. Numerical computations revealed that accounting for the effect of thermoelastic stresses of the unperturbed state on the stability region is essential. The computational results of the critical velocity for the combined effect of the temperature field parameters and various values of geometric parameters are presented.


stability, temperature field, supersonic flow, flutter


  1. Vlasov V.Z. Obshchaya teoriya obolochek i ee prilozheniya v tekhnike (The General Theory of Shells and its Applications in Engineering), Moscow, Gostekhteorizdat, 1949, 784 p.

  2. Ashley H., Zartarian C. Piston theory — a new aerodynamic tool for the aeroelastician, Journal of Aeronautical Science, 1956, vol. 23, no. 6, pp. 1109 – 1118.

  3. Bolotin V.V. Nekonservativnye zadachi teorii uprugoi ustoichivosti (Non-conservative problems of the elastic stability theory), Moscow, Fizmatgiz, 1961, 339 p.

  4. Novatskii V. Voprosy termouprugosti (Issues of thermoelasticity), Moscow, Izd-vo AN SSSR, 1962, 364 p.

  5. Bagdasaryan G.E., Mikilyan M.A., Sagoyan R.O. Izvestiya NAN RA. Mekhanika, 2011, vol. 64, no. 4, pp. 51 – 67.

  6. Bagdasaryan G.E. Kolebaniya i ustoichivost’ magnitouprugikh system (Vibrations and Stability of Magneto-elastic Systems), Erevan, Erevanskii gosudarstvennyi universitet, 1999, 440 p.

  7. Baghdasaryan G., Mikilyan M., Saghoyan R., Marzocca P. Thermoelastic stability of closed cylindrical shell in supersonic gas flow, Transactions of Nanjing University of Aeronautics and Astronautics, 2014, vol. 31, no. 2, pp. 195 – 199.

  8. Lur’e S.A., Dudchenko A.A., Nguen D.K. Trudy MAI, 2014, no. 75, available at:

  9. Shitov S.V. Trudy MAI, 2015, no. 82, available at:

  10. Egorov I.A. Trudy MAI, 2016, no. 86, available at:

  11. Amabili M., Pellicano F. Nonlinear supersonic flutter of circular cylindrical shells, AIAA Journal, 2001, vol. 39, no. 4, pp. 564 – 573.

  12. Amabili M., Paidoussis P. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with find without fluid-structure interaction, Applied Mechanics Reviews, 2003, vol. 56, pp. 349 – 381.

  13. Bismarck-Nasr M.N., Bones C. Al. Damping effects in nonlinear panel flutter, AIAA Journal, 2000, vol. 38, no. 4, pp. 711 – 713.

  14. Sargsyan S.H. On Some Interio and Boundary Effects in Thin Plates Based on the Asymmetric Theory of Elasticity, Lectures Notes in Applied and Computational Mechanics, 2004, vol. 16, pp. 201 – 210.

  15. Sargsyan S.H. The General Theory of Madnetothermoelasticity of Thin Shells, Journal of Thermal Stresses, 2011, vol. 34, no. 7, pp. 611 – 625.

  16. Yamaguchi N.,Yakota K., Tsugjimoto Y. Flutter limits and behaviors of a flexible thin sheet in high-speed flow. I. Analytical method for prediction of the sheet behavior. II. Ekhperimental results and predicted behaviors for low mass rations, Transactions of the ASME, Journal of Fluids Engineering, 2000, vol. 122, no. 1, pp. 65 – 83.

  17. Librescu L. Nonlinear magnetothermoelasticity of anisotropic plates immersed in a
    magnetic field, Journal of Thermal Stresses, 2003, vol. 26(11–12), pp. 1277 – 1304.

  18. Librescu L., Hasanyan D.J., Ambur D.R. Electromagnetically conducting elastic plates in a magnetic field: modeling and dynamic implications, International Journal of Non-Linear Mechanics, 2004, vol. 39, pp. 723 – 739.

  19. Qin Z. Magnetoelastic modeling of circular cylindrical shells immersed in a magnetic field. Part I: magnetoelastic loads considering finite dimensional effects, International Journal of Engineering Science, 2003, no. 17, pp. 2005 – 2049.

  20. Singh K., Tipton C.R., Han E., Mullin T. Magneto-elastic buckling of an Euler beam, Proc. Roy. Soc. A: Math. Phys. Eng. Sci., 2013, vol. 469(2155), article no. 20130111.

  21. Panteleev A.V., Rybakov K.A., Sotskova I.L. Spektral’nyi metod analiza nelineinykh stokhasticheskikh sistem upravleniya (Spectral method for nonlinear stochastic control systems analysis), Moscow, Vuzovskaya kniga, 2015, 392 c.

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