Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems  

作　　者：陈衍茂 刘济科 

机构地区：[1]Department of Mechanics,Sun Yat-sen University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第2期199-206,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10772202);the Doctoral Foundation of Ministry of Education of China (No.20050558032);the Natural Science Foundation of Guangdong Province (Nos.07003680 and 05003295)

摘　　要：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.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.

关 键 词：nonlinear flutter Hopf bifurcation SUPERCRITICAL SUBCRITICAL limit cycle oscillation 

分 类 号：O322[理学—一般力学与力学基础]