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

The homotopy analysis method (HAM) is employed to propose a highlyaccurate technique for solving strongly nonlinear aeroelastic systems of airfoils insubsonic 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 ofthe series. Importantly, all these equations are linear except the first one. Using someroutine procedures to deduce these equations, an obstacle would arise in expandingsome fractional functions as series in the embedding parameter. To this end, anapproach is proposed for the expansion of fractional function. This provides us with asimple yet efficient iteration scheme to seek very-high-order approximations.Numerical examples show that the HAM solutions are obtained very precisely. At thesame time, the CPU time needed can be significantly reduced by using the presentedapproach rather than by the usual procedure in expanding fractional functions