An Investigation of the Aeroelastic Response of a Two-Dimensional, Structurally Nonlinear Airfoil Subject to External Excitation

Abstract

The results of an analytical investigation are presented for the aeroelastic response of a two-dimensional, structurally nonlinear airfoil subject to a forced excitation. The system is modeled as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap motion is used to provide the forcing input to the system. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion for the aeroelastic system are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. The time-histories are analysed using Fourier transform-based techniques to obtain frequency-domain response and transfer functions. Results show that the nonlinear response of the aeroelastic system contains frequencies other than the forcing frequency. When modal frequencies and damping values are calculated using standard Fourier-based techniques, it is shown that the super- and sub-harmonic frequency content in the nonlinear response can contribute to errors when results are compared to those obtained for the equivalent linear system. This paper describes an investigation of a method of analysis that, while based on the Fourier transform, has been modified to recognize and accommodate the nonlinear contribution to the system response. The method, developed by Bendat [1], uses a band-limited random input and separates the linear and nonlinear components of the response within the frequency domain. Results are given for the application of this method to the specific case of the structurally nonlinear aeroelastic system. It is shown that the method may be used to successfully recover the linear frequency response function using the input and output data for the nonlinear system.