The flutter of an airfoil with cubic structural and aerodynamic non-linearities |
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| Affiliation: | 1. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116023, China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China;3. Advanced Technology for Aerospace Vehicles of Liaoning Province, Dalian University of Technology, Dalian 116023, China;1. College of Astronautics, Northwestern Polytechnical University, Xi''an, 710072, PR China;2. Center for Aerospace Research & Education, University of California, Irvine, USA;1. College of Astronautics, Northwestern Polytechnical University, Xi׳an 710072, PR China;2. Center for Aerospace Research & Education, University of California, Irvine, USA;1. Department of Biomedical Engineering, University of Baghdad, Baghdad, Iraq;2. Duke University, Durham, NC, United States;3. Department of Mechanical Engineering, University of Baghdad, Baghdad, Iraq |
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| Abstract: | The flutter of a two-dimensional airfoil in a supersonic flow field, with cubic structural and aerodynamic non-linearities, is investigated using an efficient algorithm of normal form, which combines the normal form theory and the center manifold theory together. First, the stability of the linearized system is analyzed in the neighborhood of an equilibrium point, which shows that the flutter instability is resulted by the Hopf bifurcation. Then the normal form of Hopf bifurcation is deduced by applying the symbolic procedure of the new normal form algorithm to the perturbation equations. Analyzing the obtained coefficients of normal form shows that for a given system, the Hopf bifurcation can change from super-critical type to sub-critical type, consequently the flutter instability changes from “benign” type to “catastrophic” type, as the flight Mach number increases. Numerical simulations verify the dependence of response on initial conditions. Finally, the effects of the structural and aerodynamic parameters on the character of flutter instability are analyzed. |
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