Supersonic Panel Flutter Analysis Assuming Effects of Initial Structural Stresses

  • Sadegh AmirzadeganEmail author
  • Seyyed Mohammad Mousavi Safavi
  • Amir Jafarzade
Original Contribution


The work is devoted to studying the stability of an elastic plate in a supersonic gas flow. This problem arises in the study of the phenomenon of panel flutter, buckling and vibration intensity of airplane and missile thin-walled structures, excited by their interaction with the airflow at high-speed flight. It is important to avoid the panel flutter occurrence to increase the structure lifetime. The vibrations of a rectangular isotropic thin plate in a supersonic airflow are studied to find the flutter speed and analyze it. Using Bubnov–Galerkin method and aerodynamic model by piston theory in supersonic fluid dynamics, effects of longitudinal and lateral stresses on the divergence speed and flutter characteristics of the panel have been analyzed by MATLAB coding. To this end, by finding the panel vibration natural frequencies and drawing the vibration graphs, flutter speed has been determined and stress effects on this speed have been discussed. The numerical results show that initial in-plane stresses have a significant effect on flutter speed of the plate. Compressive longitudinal stress will increase the panel dynamical instability, and stretching stress in this direction will decrease it. Furthermore, compressive stresses in lateral (perpendicular to the flow) direction will decrease the panel dynamical stability, and stretching stress in this direction will increase it. Using this information, the most dynamic stable and unstable zones in airplane structures can be determined.


Panel flutter Bubnov–Galerkin method Piston theory Supersonic flow Thin-walled structures High-frequency vibration 

List of Symbols


Plate length


Plate width


Bending stiffness of the plate


Plate thickness


Mach number


In-plane stress




Dynamic pressure


Air velocity


Plate deflection


(M2 − 1)1/2


The nondimensional dynamic pressure (2qa3/)


Air density



  1. 1.
    M.W. Kehoe, Historical overview of flight flutter testing, in NASA Technical Memorandum (1995)Google Scholar
  2. 2.
    E.H. Dowell, Aeroelasticity of Plates and Shells (Noordhoff International Publishing, Springer, Berlin, 1974)zbMATHGoogle Scholar
  3. 3.
    E. Ventsel, T. Krauthammer, Thin Plates and Shells Theory, Analysis, and Applications (Marcel Dekker, Inc., New York, Basel, 2001)CrossRefGoogle Scholar
  4. 4.
    M. Tawfik, Different Finite Element Models for Plate Free Vibration-Comparative Study (PEADC, Alexandria, 2004)Google Scholar
  5. 5.
    S.M. Hasheminejad, M.A. Motaaleghi, Aeroelastic analysis and active flutter suppression of an electro-rheological sandwich cylindrical panel under yawed supersonic flow. Aerosp. Sci. Technol. 42, 118–127 (2015)CrossRefGoogle Scholar
  6. 6.
    M.-C. Meijer, Aeroelastic prediction for missile fins in supersonic flows, in 29th Congress of the International Council of the Aeronautical Science, Russia (2014)Google Scholar
  7. 7.
    V.V. Vedeneev, Panel flutter at low supersonic speeds. J. Fluids Struct. 29, 79–96 (2012)CrossRefGoogle Scholar
  8. 8.
    H. Zhao, D. Cao, Supersonic flutter of laminated composite panel in coupled multi-fields. Aerosp. Sci. Technol. 47, 75–85 (2015)CrossRefGoogle Scholar
  9. 9.
    J.G. Eisley, Nonlinear vibration of beams and rectangular plates. J. Appl. Math. Phys. 15(2), 167–175 (1964)MathSciNetzbMATHGoogle Scholar
  10. 10.
    I.B. Elishakoff, Vibration analysis of clamped square orthotropic plate. AIAA J. 12, 921–924 (1974)CrossRefGoogle Scholar
  11. 11.
    Abdel-Motagaly et al., Nonlinear flutter of composite panels under yawed supersonic flow using finite elements. AIAA J. 37(9), 1025–1032 (1999)CrossRefGoogle Scholar
  12. 12.
    E.H. Dowell, H.M. Voss, Theoretical and experimental panel flutter studies in the Mach number range 1.0 to 5.0. AIAA J. 3(12), 2292–2304 (1965)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2019

Authors and Affiliations

  • Sadegh Amirzadegan
    • 1
    Email author
  • Seyyed Mohammad Mousavi Safavi
    • 1
  • Amir Jafarzade
    • 1
  1. 1.Kazan National Research Technical University (Tupolev) - KAI (KNRTU-KAI)KazanRussia

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