摘要：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.
