Time-domain Analytical Method for Aeroelastic Analysis of High Aspect Ratio Wing Using Unsteady Indicial Aerodynamics

Abstract

This paper deals with the development of a novel time-domain analytical method to perform an aeroelastic stability analysis of a high aspect ratio wing. The aerodynamic model in this paper is built upon the frequency domain of Theodorsen aerodynamics. An inverse Fourier transform technique is applied to convert the Theodorsen frequency domain transfer function to the Wagner time-domain response function. Later, lift and moment expressions, containing aerodynamic lag states are obtained using the indicial function approach which performs the convolution of the unit step response Wagner lift function with arbitrary input and its time derivative using the principle of superposition. Additional equations containing the derivative of aerodynamic lag states are coupled with previously obtained lift and moment expressions to fully get the complete unsteady aerodynamic model in the time-domain. This time-domain unsteady aerodynamic model is then coupled with a combined bending torsion beam finite element model, using the state space approach. A complex eigenvalue analysis of this state space system is performed, using MATLAB, to determine both the static and dynamic aeroelastic stability boundary. Finally, in this paper, aeroelastic stability analysis of the high aspect ratio wing is performed using the current method and results are validated with MSC Nastran aeroelastic analysis and those available in the literature.