Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter syste

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Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems

The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated,with the flow speed as the bifurcation parameter.The center manifold theory and complex normal form method are 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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作 者: CHEN Yan-mao LIU Ji-ke  
作者单位:Department of Mechanics,Sun Yat-sen University,Guangzhou 510275,P.R.China 
刊 名:应用数学和力学(英文版)  EI SCI
英文刊名:APPLIED MATHEMATICS AND MECHANICS 
年,卷(期):2008 29(2) 
分类号:O322 
关键词:nonlinear flutter   Hopf bifurcation   supercritical   subcritical   limit cycle oscillation  
机标关键词:bifurcation equationequivalent linearizationHopf bifurcationharmonic balancecenter manifoldnormal form 
基金项目:国家自然科学基金,高等学校博士学科点专项科研项目,广东省自然科学基金 
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