SolutionofTwo-DimensionalAirfoilFlutterEquationsUsing.pdfVIP

Dynamical Systems and Control 动力系统与控制, 2016, 5(3), 105-113 Published Online July 2016 in Hans. /journal/dsc /10.12677/dsc.2016.53012 文章引用: 王云海, 季雨, 蔡群, 张宪明. 求解二元机翼颤振方程的切比雪夫展式方法[J]. 动力系统与控制, 2016, 5(3): 105-113. /10.12677/dsc.2016.53012 Solution of Two-Dimensional Airfoil Flutter Equations Using Chebyshev Expansion Method Yunhai Wang1, Yu Ji2, Qun Cai1, Xianming Zhang1 1College of Mechanical Engineering, Guizhou Institute of Technology, Guiyang Guizhou 2Institute of Vibration Engineering Research, State Key Lab of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu Received: Jun. 29th, 2016; accepted: Jul. 24th, 2016; published: Jul. 27th, 2016 Copyright ? 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract The classical two-dimensional airfoil flutter equations can be established by using sinusoidal structure motion hypothesis and some kinds of aerodynamic theory. In fact, when flutter occurs, structure movement is likely to be more complex. Sinusoidal structure hypothesis is proposed merely because it is simple and easy to use. For this case, harmonic balance method cannot ap- propriate for all the higher order terms are ignored, which might lead to larger error. This paper presents a new way to establish the flutter equations: Chebyshev expansion method. This method which is suitable for quantitative questions has higher accuracy than harmonic balance, moreover, it is applicable to the analysis of those qualitative of nonlinear problems as well. Finally, an exam- ple is used to illustrate how to establish the flutter equations of two-dimension airfoil by using Chebyshev expansion method and how to find the flutter solution based on V-g method. Keywords Chebyshev Expansion, Flutter, Unsteady Aerodynamics 求解二元机翼颤振方程的切比雪夫展式方法 王云海1，季 雨2，蔡