Analytical nonlinear flutter and sensitivity analysis of aircraft wings subjected to a transverse follower force

In the present study, the nonlinear aeroelastic and sensitivity analysis of high aspect ratio wings subjected to a transverse follower force are discussed. A nonlinear structural model of wings is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations of motions are obtained via Hamilton’s principle and Galerkin method. Utilizing the method of multiple-scales, analytical approximate flutter response of the system is obtained. For validation, the analytical solution is compared with numerical solution and good agreement is observed. The time history of the tip displacement and tip twist solution are plotted for different airspeeds. Effects of follower force and its spanwise location and also the wing geometric characteristics on the flutter margin are discussed. Moreover, flutter margin sensitivity to different design parameters is analyzed. Results indicate that increasing the wing chord makes the system unstable. Furthermore, according to the analytical solution, effects of the wing chord and mass per unit length on the flutter margins are more important than the other system parameters.