Skip to main content
SpringerLink
Log in

An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We perform an analytical and experimental investigation into the dynamics of an aeroelastic system consisting of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The experimental results show that the onset of flutter takes place at a speed smaller than the one predicted by a quasi-steady aerodynamic approximation. On the other hand, the unsteady representation of the aerodynamic loads accurately predicts the experimental value. The linear analysis details the difference in both formulation and provides an explanation for this difference. Nonlinear analysis is then performed to identify the nonlinear coefficients of the pitch spring. The normal form of the Hopf bifurcation is then derived to characterize the type of instability. It is demonstrated that the instability of the considered aeroelastic system is supercritical as observed in the experiments.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Dowell, E.H., Tang, D.: Nonlinear aeroelasticity and unsteady aerodynamics. AIAA J. 40, 1697–1707 (2002)

    Article  Google Scholar 

  2. Gilliat, H.C., Strganac, T.W., Kurdila, A.J.: An investigation of internal resonance in aeroelastic systems. Nonlinear Dyn. 31, 1–22 (2003)

    Article  Google Scholar 

  3. Raghothama, A., Narayanan, S.: Non-linear dynamics of a two-dimensional air foil by incremental harmonic balance method. J. Sound Vib. 226, 493–517 (1999)

    Article  Google Scholar 

  4. Liu, L., Wong, Y.S., Lee, B.H.K.: Application of the centre manifold theory in non-linear aeroelasticity. J. Sound Vib. 234, 641–659 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Abdelkefi, A., Vasconcellos, R., Marques, F., Hajj, M.R.: Bifurcation analysis of an aeroelastic system with concentrated nonlinearities. Nonlinear Dyn. 69, 57–70 (2012)

    Article  Google Scholar 

  6. Abdelkefi, A., Vasconcellos, R., Marques, F., Hajj, M.R.: Modeling and identification of freeplay nonlinearity. J. Sound Vib. 331, 1898–1907 (2012)

    Article  Google Scholar 

  7. Vasconcellos, R., Abdelkefi, A., Marques, F., Hajj, M.R.: Representation and analysis of control surface freeplay nonlinearity. J. Fluids Struct. 31, 79–91 (2012)

    Article  Google Scholar 

  8. Erturk, A., Vieira, W.G.R., De Marqui, C., Inman, D.J.: On the energy harvesting potential of piezoaeroelastic systems. Appl. Phys. Lett. 96, 184103 (2010)

    Article  Google Scholar 

  9. Abdelkefi, A., Nayfeh, A.H., Hajj, M.R.: Modeling and analysis of piezoaeroelastic energy harvesters. Nonlinear Dyn. 67, 925–939 (2012)

    Article  Google Scholar 

  10. Abdelkefi, A., Nayfeh, A.H., Hajj, M.R.: Design of piezoaeroelastic energy harvesters. Nonlinear Dyn. 68, 519–530 (2012)

    Article  Google Scholar 

  11. Abdelkefi, A., Nayfeh, A.H., Hajj, M.R.: Enhancement of power harvesting from piezoaeroelastic systems. Nonlinear Dyn. 68, 531–541 (2012)

    Article  Google Scholar 

  12. Souza, V.C., Anicezio, M., De Marqui, C., Erturk, A.: Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment. J. Smart Mater. Struct. 20, 094007 (2011)

    Article  Google Scholar 

  13. Abdelkefi, A., Hajj, M.R., Nayfeh, A.H.: Sensitivity analysis of piezoaeroelastic energy harvesters. J. Intell. Mater. Syst. Struct. (2012). doi:10.1177/1045389X12440752

    Google Scholar 

  14. Strganac, T.W., Ko, J., Thompson, D.E., Kurdila, A.J.: Identification and control of limit cycle oscillations in aeroelastic systems. In: Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit (1999). AIAA Paper No. 99-1463

    Google Scholar 

  15. Ko, J., Strganac, T.W., Kurdila, A.J.: Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity. Nonlinear Dyn. 18, 289–301 (1999)

    Article  MATH  Google Scholar 

  16. Gilliatt, H.C., Straganac, T.W., Kurdilla, A.J.: An investigation of internal resonance in aeroelastic systems. Nonlinear Dyn. 31, 1–22 (2003)

    Article  MATH  Google Scholar 

  17. Fung, Y.C.: An Introduction to the Theory of Aeroelasticity. Dover, New York (1993)

    Google Scholar 

  18. Dowell, E.H.: A Modern Course in Aeroelasticity. Kluwer, Dordrecht (1995)

    MATH  Google Scholar 

  19. Theodorsen, T.: General theory of aerodynamic instability and the mechanism of flutter. Technical Report NACA 496 (1935)

  20. Bisplinghoff, R.L., Ashley, H.A., Halfman, R.L.: Aeroelasticity. Dover, New York (1996)

    Google Scholar 

  21. Edwards, J.W., Ashley, A.H., Breakwell, J.V.: Unsteady aerodynamic modeling for arbitrary motions. AIAA J. 17, 365–374 (1979)

    Article  MATH  Google Scholar 

  22. Nayfeh, A.H.: Perturbation Methods. Wiley, New York (1973)

    MATH  Google Scholar 

  23. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley-Interscience, New York (1981)

    MATH  Google Scholar 

  24. Nayfeh, A.H., Balachandran, B.: In: Applied nonlinear dynamics. Wiley Series in Nonlinear Science. Wiley, New York (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Abdessattar Abdelkefi, Ali H. Nayfeh & Muhammad R. Hajj

  2. Laboratory of Aeroelasticity, University of Sao Paulo, São Carlos, Brazil

    Rui Vasconcellos

Authors
  1. Abdessattar Abdelkefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui Vasconcellos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali H. Nayfeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad R. Hajj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad R. Hajj.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abdelkefi, A., Vasconcellos, R., Nayfeh, A.H. et al. An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system. Nonlinear Dyn 71, 159–173 (2013). https://doi.org/10.1007/s11071-012-0648-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0648-z

Keywords

Search

Navigation