Skip to main content Accessibility help

Random Flutter of Multi-Stable Airfoils Excited Parametrically in Steady Flows

  • Y. Hao (a1) and Z. Q. Wu (a2)


In this article, random flutter of multi-stable airfoils in steady flow is investigated by means of the analytical method for stochastic P-bifurcation, where the effect of the stochastic disturbance in the generalized flow speed on the airfoils is considered. The results show that under constant stochastic disturbance intensity, the coherence resonance could be induced by the variation of generalized flow speed. In addition, if the generalized flow speed keeps unchanged and its stochastic disturbance is sufficiently large, the response of the system will tend to be a stable equilibrium. It indicates that the parametric stochastic disturbance is effective to maintain system stability. Moreover, it is shown in this paper that the analytical method for stochastic P-bifurcation can be extended to study stochastic P-bifurcations in other high-dimensional systems.


Corresponding author

*Corresponding author (


Hide All
1.Price, S. J. and Alighanbari, H., “The Aeroelastic Response of a Two-Dimensional Airfoil with Bilinear and Cubic Structural Nonlinearities,” Journal of Fluids and Structures, 9, pp. 175193 (1995).
2.Poirel, D. C. and Price, S. J., “Post-Instability Behavior of a Structurally Nonlinear Airfoil in Longitudinal Turbulence,” Journal of Aircraft, 34, pp. 619627 (1997).
3.Lee, B. H. K., Price, S. J. and Wong, Y. S., “Nonlinear Aeroelastic Analysis of Airfoils: Bifurcation and Chaos,” Progress in Aerospace Sciences, 35, pp. 205334 (1999).
4.Poirel, D. C. and Price, S. J., “Structurally Nonlinear Fluttering Airfoil in Turbulent Flow [J],” AIAA Journal, 39, pp. 19601968 (2001).
5.Poirel, D. and Price, S. J., “Response Probability Structure of a Structurally Nonlinear Fluttering Air-foil in Turbulent Flow,” Probabilistic Engineering Mechanics, 18, pp. 185202 (2003).
6.Poirel, D. and Price, S. J., “Bifurcation Characteristics of a Two-Dimensional Structurally Non-Linear Airfoil in Turbulent Flow,” Nonlinear Dynamics, 48, pp. 423435 (2007).
7.Poirel, D., Harris, Y. and Benaissa, A., “Self- Sustained Aeroelastic Oscillations of a NACA0012 Airfoil at Low-to-Moderate Reynolds Numbers,” Journal of Fluids and Structures, 24, pp. 700719 (2008).
8.Poirel, D. and Yuan, W., “Aerodynamics of Laminar Separation Flutter at a Transitional Reynolds Number,” Journal of Fluids and Structures, 26, pp. 11741194 (2010).
9.Poirel, D. and Mendes, F., “Experimental Small- Amplitude Self-Sustained Pitch–Heave Oscillations at Transitional Reynolds Numbers [J],” AIAA Journal, 52, pp. 15811590 (2014).
10.Yuan, W., Poirel, D. and Wang, B., “Simulations of Pitch–Heave Limit-Cycle Oscillations at a Transitional Reynolds Number,” AIAA Journal, 51, pp. 17161732 (2013).
11.Huang, Y., Fang, C. and Liu, X., “On Stochastic Dynamical Behaviors of Binary Airfoil with Nonlin Ear Structure,” Acta Aeronautica et Astronautica Sinica, 31, pp. 19461952 (2010).
12.Zhao, D. M., Zhang, Q. C. and Tan, Y., “Random Flutter of a 2-DOF Nonlinear Airfoil in Pitch and Plunge with Freeplay in Pitch,” Nonlinear Dynamics, 58, pp. 643654 (2009).
13.Yang, Z. C. and Zhao, L. C., “Analysis of Limit Cycle Flutter of an Airfoil in Incompressible Flow,” Journal of Sound and Vibration, 123, pp. 113 (1988).
14.Berggren, D., “Investigation of Limit Cycle Oscillations for a Wing Section with Nonlinear Stiffnes,” Aerospace Science and Technology, 8, pp. 2734 (2004).
15.Chassaing, J. C., Lucor, D. and Gon, J. T., “Stochastic Nonlinear Aeroelastic Analysis of Asupersonic Lifting Surface Using an Adaptive Spectual Method,” Journal of Sound and Vibration, 331, pp. 394411 (2012).
16.Dowell, E. H., Thomas, J. P. and Hall, K. C., “Transonic Limit Cycle Oscillation Analysis Using Reduced Order Aerodynamic Models,” Journal of Fluids and Structures, 19, pp. 1727 (2004).
17.Christiansen, L. E. et al., “Nonlinear Characteristics of Randomly Excited Transonic Flutter,” 58, pp. 385405 (2002).
18.Missoum, S., Dribusch, C. and Beran, P., “Reliability- Based Design Optimization of Nonlinear Aeroelasticity Problems,” Journal of Aircraft, 47, pp. 992998 (2010).
19.Dribush, C., “Multi-Fidelity Construction of Explicit Boundaries: Application to Aeroelasticity,” University of Arizone, 2013.
20.Dribusch, C., Missoum, S. and Beran, P., “A Multifidelity Approach for the Construction of Explicit Decision Boundaries: Application to Aeroelasticity,” 42, pp. 693705 (2010).
21.Dimitriadis, G. and Li, J., “Bifurcation Behavior of Airfoil Undergoing Stall Flutter Oscillations in Low- Speed Wind Tunnel,” AIAA Journal, 47, pp. 25772596 (2009).
22.Wu, Z. Q. and Zhang, J. W., “Complicated Bifurcations In Limit-Cycle Flutter Of Two-Dimensional Airfoil,” Engineering Mechanics, 25, pp. 5255 (2008).
23.Wang, H. L. and Wu, Z. Q., “Nonlinear Vibration of the High Dimensional Systems with Parameters,” Acta Mechanica Sinica, 28, pp. 109113 (1996).
24.Hao, Y. and Wu, Z. Q., “Stochastic P-Bifurcation of Tri-Stable Van der Pol-Duffing Osciliator,” Acta Mechanica Sinica, 45, pp. 257265 (2013).
25.Wu, Z. Q. and Hao, Y., “Three-Peak P-Bifurcation in Stochastically Excited Van der Pol-Duffing Oscillator,” Scientia Sinica Physica, Mechanica & Astronlmica, 4, pp. 524529 (2013).
26.Zakharova, A. et al., “Stochastic Bifurcations and Coherencelike Resonance in a Self-Sustained Bistable Noisy Oscillator,” Physical Review E, 81, (2010).


Random Flutter of Multi-Stable Airfoils Excited Parametrically in Steady Flows

  • Y. Hao (a1) and Z. Q. Wu (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed