| BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW |
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| 作者姓名： | LiuFei YangYiren |
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| 作者单位： | DepartmentofAppliedMechanicsandEngineering,SouthwestJiaotongUniversity,Chengdu610031,China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 10272092)
Science Foundation of Southwest Jiaotong University (No.2003B09). |
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| 摘 要： | Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.
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| 关 键 词： | 非线性系统 霍普夫分支 半稳定有限循环 机翼颤振 |
BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW |
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| LiuFei YangYiren.BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW[J].Acta Mechanica Solida Sinica,2005,18(2):157-163. |
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| Authors: | Liu Fei Yang Yken |
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| Abstract: | Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given. |
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| Keywords: | nonlinear systems airfoil flutter Hopf bifurcation 2-multiple semi-stable limit cycle bifurcation |
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