Table of Contents Author Guidelines Submit a Manuscript
Advances in Acoustics and Vibration
Volume 2011, Article ID 926271, 10 pages
http://dx.doi.org/10.1155/2011/926271
Research Article

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

1Nari Technology Development Limited Company, 20 High-Tech Road, Nanjing 210061, China
2Department of Mechanics, Sun Yat-sen University, 135 Xingang Road, Guangzhou 510275, China
3State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Received 22 September 2010; Accepted 20 April 2011

Academic Editor: Kok Keong Choong

Copyright © 2011 Y. P. Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. H. K. Lee, S. J. Price, and Y. S. Wong, “Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos,” Progress in Aerospace Sciences, vol. 35, no. 3, pp. 205–334, 1999. View at Publisher · View at Google Scholar · View at Scopus
  2. J. K. Liu and L. C. Zhao, “Bifurcation analysis of airfoils in incompressible flow,” Journal of Sound and Vibration, vol. 154, no. 1, pp. 117–124, 1991. View at Google Scholar · View at Scopus
  3. Y. M. Chen and J. K. Liu, “On the limit cycles of aeroelastic systems with quadratic nonlinearities,” Structural Engineering and Mechanics, vol. 30, no. 1, pp. 67–76, 2008. View at Google Scholar · View at Scopus
  4. B. H. K. Lee, L. Liu, and K. W. Chung, “Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces,” Journal of Sound and Vibration, vol. 281, no. 3–5, pp. 699–717, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. L. P. Liu and E. H. Dowell, “The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics,” Nonlinear Dynamics, vol. 37, no. 1, pp. 31–49, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. L. Liu, E. H. Dowell, and J. P. Thomas, “A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces,” Journal of Fluids and Structures, vol. 23, no. 3, pp. 351–363, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Shahrzad and M. Mahzoon, “Limit cycle flutter of airfoils in steady and unsteady flows,” Journal of Sound and Vibration, vol. 256, no. 2, pp. 213–225, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Cai, J. K. Liu, and J. Li, “Incremental harmonic balance method for airfoil flutter with multiple strong nonlinearities,” Applied Mathematics and Mechanics (English Edition), vol. 27, no. 7, pp. 953–958, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. K. W. Chung, C. L. Chan, and B. H. K. Lee, “Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method,” Journal of Sound and Vibration, vol. 299, no. 3, pp. 520–539, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. K. W. Chung, Y. B. He, and B. H. K. Lee, “Bifurcation analysis of a two-degree-of-freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation-incremental method,” Journal of Sound and Vibration, vol. 320, no. 1-2, pp. 163–183, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Liu, Y. S. Wong, and B. H. K. Lee, “Application of the centre manifold theory in non-linear aeroelasticity,” Journal of Sound and Vibration, vol. 234, no. 4, pp. 641–659, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Q. Ding and D. L. Wang, “The flutter of an airfoil with cubic structural and aerodynamic non-linearities,” Aerospace Science and Technology, vol. 10, no. 5, pp. 427–434, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Grzedziński, “Limitation of application of the center manifold reduction in aeroelasticity,” Journal of Fluids and Structures, vol. 21, no. 2, pp. 187–209, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. S. J. Liao, “A kind of approximate solution technique which does not depend upon small parameters-II: an application in fluid mechanics,” International Journal of Non-Linear Mechanics, vol. 32, no. 5, pp. 815–822, 1997. View at Google Scholar · View at Scopus
  15. S. J. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, Fla, USA, 2003.
  17. T. Pirbodaghi, M. T. Ahmadian, and M. Fesanghary, “On the homotopy analysis method for non-linear vibration of beams,” Mechanics Research Communications, vol. 36, no. 2, pp. 143–148, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. M. Chen and J. K. Liu, “A study of homotopy analysis method for limit cycle of van der Pol equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 1816–1821, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. B. T. Kennedy, D. C. Weggel, D. M. Boyajian, and R. E. Smelser, “Closed-form solution for a cantilevered sectorial plate subjected to a twisting tip moment,” Mechanics Research Communications, vol. 35, no. 8, pp. 491–496, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. M. Chen and J. K. Liu, “Uniformly valid solution of limit cycle of the Duffing-van der Pol equation,” Mechanics Research Communications, vol. 36, no. 7, pp. 845–850, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. M. Chen and J. K. Liu, “Homotopy analysis method for limit cycle flutter of airfoils,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 854–863, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. Y. M. Chen and J. K. Liu, “Homotopy analysis method for limit cycle oscillations of an airfoil with cubic nonlinearities,” JVC/Journal of Vibration and Control, vol. 16, no. 2, pp. 163–179, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. S. J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2003–2016, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. Z. Niu and C. Wang, “A one-step optimal homotopy analysis method for nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2026–2036, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. H. Qian and S. M. Chen, “Accurate approximate analytical solutions for multi-degree-of-freedom coupled van der Pol-Duffing oscillators by homotopy analysis method,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 3113–3130, 2010. View at Publisher · View at Google Scholar · View at Scopus