Aeroelastic Stability Analysis of Aircraft Wings with High Aspect Ratios by Transfer Function Method

A new method is developed for the aeroelastic stability analysis of a high-aspect-ratio wing based on the transfer function. First, the flutter governing equations for three types of wing elements including clear wing element, wing element with a control surface and that with an external store are, respectively, established by combining the corresponding bend-twist vibration model with the Theodrosen's unsteady aerodynamic model. Then, in order to use the transfer function method, the element governing equations are processed by the Fourier transform and are formulated in a state-space form using state vector. Based on the finite element procedure, the global governing equations of the whole wing are obtained. Both the flutter velocity and flutter frequency are derived by solving a complex eigenvalue problem with the graphical approach. Additionally, the torsional divergence of the high-aspect-ratio wing is obtained by solving a real eigenvalue problem, which is a degenerated form of the wing flutter governing equations. Finally, illustrative examples are prepared to demonstrate the validity of the present method, which is insensitive to mesh density and does not require structural modal analysis for aeroelastic stability.