Nonlinear aeroelastic response of slender wings based on Wagner function

Abstract

This paper presents a method for nonlinear aeroelastic analysis of Human Powered Aircraft (HPA) wings. In this type of aircraft there is a long, highly flexible wing. Wing flexibility, coupled with long wing span can lead to large deflections during normal flight operation; therefore, a wing in vertical and torsional motion using the second-order form of nonlinear general flexible Euler–Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic theory based on Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulations yields the nonlinear integro-differentials aeroelastic equations. Using the Galerkin's method and modes summation technique, the governing equations will be solved by introducing an iterative numerical method to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of linear study which shows good agreement for speeds less than the flutter speed, but the nonlinear model shows limit cycle oscillations for the wing beyond the flutter boundary.