Dynamic analysis of an aeroelastic airfoil with freeplay nonlinearity by precise integration method based on Padé approximation

An improved precise integration method (PIM) incorporated with Padé approximation (PadéPIM) is proposed, and the aeroelastic behavior of an aeroelastic airfoil with freeplay nonlinearity is investigated by using the PadéPIM method. For the aeroelastic system with this non-smooth nonlinearity, a predictor-correction algorithm is adopted to avoid the numerical inaccuracy induced by the crossover of the switching points of freeplay nonlinearity. The comparative studies for the PadéPIM method and other conventional numerical methods, such as the classical fourth-order Runge–Kutta (RK4) method, the RK4 method combined with the Henon’s method and the original PIM, which is based on the Taylor series expansion, are performed for the solution of dynamic responses of the aeroelastic airfoil. Numerical results verify that the PadéPIM method is unconditionally stable and has higher accuracy and efficiency than other methods, especially with high reliability for obtaining complex dynamic responses. When freeplays in pitch/plunge degrees-of-freedom are further considered for nonlinear aeroelastic characteristics of the aeroelastic airfoil, the regions of limit cycle oscillation and chaotic motions are detected for speeds below the stability boundary of the system predicted by linear theory. Results of the present study show that the existence of these regions is strongly dependent on the freeplay magnitudes, which have significant effects on the aeroelastic responses. These nonlinear aeroelastic behaviors exhibited in the system with multiple freeplay nonlinearities are greatly different from that with single freeplay nonlinearity. It has also been shown that the appropriate combinations of multiple freeplays can be selected for eliminating the complex dynamic responses of the aeroelastic airfoil.