CHEN Yan-mao, LIU Ji-ke. Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems[J]. Applied Mathematics and Mechanics, 2008, 29(2): 181-187.
Citation: CHEN Yan-mao, LIU Ji-ke. Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems[J]. Applied Mathematics and Mechanics, 2008, 29(2): 181-187.

Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems

  • Received Date: 2007-08-15
  • Rev Recd Date: 2008-01-03
  • Publish Date: 2008-02-15
  • The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated with the flow speed as a bifurcation parameter.The center manifold theory and complex normal form method were used to obtain the bifurcation equation.Interestingly,for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical.It is found,mathematically,this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter.The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
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