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

Published online by Cambridge University Press:  02 July 2018

Y. Hao
Affiliation:
College of Civil Engineering & Mechanics Yanshan UniversityQinhuangdao, China
Z. Q. Wu*
Affiliation:
School of Mechanical Engineering Tianjin UniversityTianjin, China
*
*Corresponding author (zhiqwu@tju.edu.cn)
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Abstract

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.

Type
Research Article
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

REFERENCES

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).Google Scholar
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).Google Scholar
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).Google Scholar
Poirel, D. C. and Price, S. J., “Structurally Nonlinear Fluttering Airfoil in Turbulent Flow [J],” AIAA Journal, 39, pp. 19601968 (2001).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
Poirel, D. and Yuan, W., “Aerodynamics of Laminar Separation Flutter at a Transitional Reynolds Number,” Journal of Fluids and Structures, 26, pp. 11741194 (2010).Google Scholar
Poirel, D. and Mendes, F., “Experimental Small- Amplitude Self-Sustained Pitch–Heave Oscillations at Transitional Reynolds Numbers [J],” AIAA Journal, 52, pp. 15811590 (2014).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
Berggren, D., “Investigation of Limit Cycle Oscillations for a Wing Section with Nonlinear Stiffnes,” Aerospace Science and Technology, 8, pp. 2734 (2004).Google Scholar
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).Google Scholar
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).Google Scholar
Christiansen, L. E. et al., “Nonlinear Characteristics of Randomly Excited Transonic Flutter,” 58, pp. 385405 (2002).Google Scholar
Missoum, S., Dribusch, C. and Beran, P., “Reliability- Based Design Optimization of Nonlinear Aeroelasticity Problems,” Journal of Aircraft, 47, pp. 992998 (2010).Google Scholar
Dribush, C., “Multi-Fidelity Construction of Explicit Boundaries: Application to Aeroelasticity,” University of Arizone, 2013.Google Scholar
Dribusch, C., Missoum, S. and Beran, P., “A Multifidelity Approach for the Construction of Explicit Decision Boundaries: Application to Aeroelasticity,” 42, pp. 693705 (2010).Google Scholar
Dimitriadis, G. and Li, J., “Bifurcation Behavior of Airfoil Undergoing Stall Flutter Oscillations in Low- Speed Wind Tunnel,” AIAA Journal, 47, pp. 25772596 (2009).Google Scholar
Wu, Z. Q. and Zhang, J. W., “Complicated Bifurcations In Limit-Cycle Flutter Of Two-Dimensional Airfoil,” Engineering Mechanics, 25, pp. 5255 (2008).Google Scholar
Wang, H. L. and Wu, Z. Q., “Nonlinear Vibration of the High Dimensional Systems with Parameters,” Acta Mechanica Sinica, 28, pp. 109113 (1996).Google Scholar
Hao, Y. and Wu, Z. Q., “Stochastic P-Bifurcation of Tri-Stable Van der Pol-Duffing Osciliator,” Acta Mechanica Sinica, 45, pp. 257265 (2013).Google Scholar
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).Google Scholar
Zakharova, A. et al., “Stochastic Bifurcations and Coherencelike Resonance in a Self-Sustained Bistable Noisy Oscillator,” Physical Review E, 81, (2010).Google Scholar