Bending-torsional flutter of wings with an attached mass subjected to a follower force

The bending-torsional flutter characteristics of a wing containing an arbitrarily placed mass under a follower force are presented. The governing equations and boundary conditions are determined via Hamiltonʹs variational principle. In order to precisely consider the spanwise and chordwise locations and the properties of the attached external mass and the follower force, the generalized function theory is used. Unsteady aerodynamic pressure loadings are also considered. The resulting partial differential equations are transformed into a set of eigenvalue equations through the extended Galerkinʹs approach. The interactions cause the model differential equations of the problem to be non-self-adjoint. As a result, if each of the parameters flow speed, follower force, or external mass exceeds a certain critical value, the wing experiences flutter instabilities. The numerical results are also compared with the published results and excellent agreement is observed. Numerical simulations highlighting the effects of the follower force and the external mass parameters such as the mass ratio and the attached locations on the flutter speed and frequency are presented.