Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method

Abstract

This paper proposed a numerical algorithm based on precise integration method to investigate the aeroelastic system of an airfoil with a freeplay. The system was split into three linear sub-systems separated by switching points related with the freeplay. A predictor–corrector algorithm was constructed to tackle the key computational obstacle in accurately searching system responses passing the switching points. With the aid of the algorithm, the precise integration method can solve the sub-systems one by one and provide solutions to any desired accuracy compared with exact solutions. Moreover, it can keep high precision with the step length increasing. The precise integration method is more accurate and efficient than the Runge–Kutta method with the same time step. In addition, the Runge–Kutta sometimes provides limit cycle oscillations, bifurcation charts or chaotic responses falsely even though the step length is much smaller than that adopted in precise integration method. Due to the high precision and efficiency, the presented approach has potential to become a benchmark for solution techniques for piecewise nonlinear dynamical systems.