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Advances in Acoustics and Vibration
Volume 2011, Article ID 926271, 10 pages
Research Article

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

1Nari Technology Development Limited Company, 20 High-Tech Road, Nanjing 210061, China
2Department of Mechanics, Sun Yat-sen University, 135 Xingang Road, Guangzhou 510275, China
3State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Received 22 September 2010; Accepted 20 April 2011

Academic Editor: Kok Keong Choong

Copyright © 2011 Y. P. Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The homotopy analysis method (HAM) is employed to propose a highly accurate technique for solving strongly nonlinear aeroelastic systems of airfoils in subsonic flow. The frequencies and amplitudes of limit cycle oscillations (LCOs) arising in the considered systems are expanded as series of an embedding parameter. A series of algebraic equations are then derived, which determine the coefficients of the series. Importantly, all these equations are linear except the first one. Using some routine procedures to deduce these equations, an obstacle would arise in expanding some fractional functions as series in the embedding parameter. To this end, an approach is proposed for the expansion of fractional function. This provides us with a simple yet efficient iteration scheme to seek very-high-order approximations. Numerical examples show that the HAM solutions are obtained very precisely. At the same time, the CPU time needed can be significantly reduced by using the presented approach rather than by the usual procedure in expanding fractional functions.