Analysis of a Two-Dimensional Aeroelastic System Using the Differential Transform Method

Abstract

This paper investigates the nonlinear responses of a typical two-dimensional airfoil with control surface freeplay and cubic pitch stiffness in an incompressible flow. The differential transform (DT) method is applied to the aeroelastic system. Due to the nature of this method, it is capable of providing analytical solutions in forms of Taylor series expansions in each subdomain between two adjacent sampling points. The results demonstrate that the DT method can successfully detect nonlinear aeroelastic responses such as limit cycle oscillations (LCOs), chaos, bifurcation, and flutter phenomenon. The accuracy and efficiency of this method are verified by comparing it with the RK (Henon) method. In addition to ordinary differential equations (ODEs), the DT method is also a powerful tool for directly solving integrodifferential equations. In this paper, the original aeroelastic system of integrodifferential equations is handled directly by the DT method. With no approximation or simplification imposed on the integral terms of aerodynamic function, the resulted solutions are closer to representing the real dynamical behavior.