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The European Physical Journal Special Topics

, Volume 222, Issue 7, pp 1707–1731 | Cite as

Analytical periodic motions in a parametrically excited, nonlinear rotating blade

  • F. Wang
  • A.C.J. Luo
Regular Article

Abstract

The stability and bifurcation analyses of periodic motions in a rotating blade subject to a torsional excitation are investigated. For high speed rotations, cubic geometric nonlinearity and gyroscopic effects of the rotating blade are considered. From the Galerkin method, the partial differential equation of the nonlinear rotating blade is simplified to the ordinary differential equations, and periodic motions and stability of the rotating blade are studied by the generalized harmonic balance method. The analytical and numerical results of periodic solutions are compared. The rich dynamics and co-existing periodic solutions of the nonlinear rotating blades are investigated.

Keywords

Periodic Solution Hopf Bifurcation European Physical Journal Special Topic Periodic Motion Energy Harvest 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Meirovitch, Analytical Methods in Vibrations (McGraw Hill, New York, 1967)Google Scholar
  2. 2.
    P.W. Likins, F.J. Barbera, V. Baddeley, AIAA J. 11, 1251 (1973)ADSCrossRefGoogle Scholar
  3. 3.
    F.R. Vigneron, AIAA J. 13, 126 (1975)ADSCrossRefGoogle Scholar
  4. 4.
    T.R. Kane, R.R. Ryan, A.K. Banerjee, AIAA. J. Guid. Control Dyn. 10, 139 (1987)ADSCrossRefGoogle Scholar
  5. 5.
    J.C. Simo, L. Vu-Quoc, J. Sound Vibr. 119, 487 (1987)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    I. Sharf, ASME J. Dynamic Syst. Meas. Control 117, 74 (1995)CrossRefzbMATHGoogle Scholar
  7. 7.
    I. Sharf, Int. J. Numerical Meth. Eng. 39, 763 (1996)CrossRefzbMATHGoogle Scholar
  8. 8.
    I. Sharf, Multibody System Dyn. 3, 189 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    M.R.M. Crespo da Silva, C.C. Glynn, Int. J. Non-Linear Mech. 13, 261 (1979)CrossRefGoogle Scholar
  10. 10.
    M.R.M. Crespo da Silva, Int. J. Solids Struct. 35, 3299 (1998)CrossRefzbMATHGoogle Scholar
  11. 11.
    A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (Wiley Interscience, New York, 1979)Google Scholar
  12. 12.
    T.J. Anderson, B. Balachandran, A.H. Nayfeh, ASME J. Vibr. Acoust. 116, 480 (1994)CrossRefGoogle Scholar
  13. 13.
    O.A. Bauchau, C.L. Bottasso, Y.G. Nikishkov, Math. Computer Model. 33, 1113 (2001)CrossRefzbMATHGoogle Scholar
  14. 14.
    A.A. Shabana, Dynamics of Multibody Systems (Cambridge University Press, 2005)Google Scholar
  15. 15.
    J. Valverde, D. García-Vallejo, Nonlinear Dyn. 55, 355 (2009)CrossRefzbMATHGoogle Scholar
  16. 16.
    J.R. Claeyssen, R.D. Copetti, J.M. Balthazar, Material Sci. Forum 440-441, 261 (2003)CrossRefGoogle Scholar
  17. 17.
    J. Warminski, J.M. Balthazar, “Nonlinear vibrations of a beam with a tip mass attached to a rotating hub”, The Proceedings of IDETC/CIE2005, Long Beach, California, September 24-28, 2005, Article No: DETC2005-84518, p. 1619Google Scholar
  18. 18.
    Y.N. Al-Nassar, B.O. Al-Bedoor, J. Sound Vibr. 259, 1237 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    Ö. Turhan, G. Bulut, J. Sound Vibr. 280, 945 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    G.K. Blanch, D.S. Clemm, Mathieu’s equation for complex parameters: tables of characteristic values (U.S. Government Print Office, 1969)Google Scholar
  21. 21.
    K. Takshashi, J. Sound Vibr. 78, 519 (1981)ADSCrossRefGoogle Scholar
  22. 22.
    A. Fenili, J.M. Balthazar, J. Sound Vibr. 282, 543 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    A. Fenilim, J.M. Balthazar, J. Sound Vibr. 46, 51 (2008)Google Scholar
  24. 24.
    A.C.J. Luo, J.Z. Huang, Int. J. Bif. Chaos 22, Article No. 1250093Google Scholar
  25. 25.
    A.C.J. Luo, Continuous Dynamical Systems (Higher Education Press, Beijing and L&H Scientific, Glen Carbon, 2012)Google Scholar
  26. 26.
    F.X. Wang, Luo A.C.J., J. Appl. Nonlinear Dynamics 1, 263 (2012)zbMATHGoogle Scholar
  27. 27.
    A.C.J. Luo, Nonlinear Deformable-body Dynamics (Higher Education Press, Beijing and Springer, Heidelberg, 2010)Google Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Mechanical and Industrial Engineering, Southern Illinois University EdwardsvilleEdwardsvilleUSA

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