Effects of Airfoil Geometry and Mechanical Characteristics on the Onset of Flutter (As a Basis for Future Work on the Effects of Structural Polynomial Nonlinearities on the Flutter Boundary)

This paper derives linear 2nd order ordinary differential equations describ-ing the motion of a 2 dimensional airfoil allowing for 3 spatial Degrees of Freedom in airfoil angular rotation, vertical movement and control surface rotation. The equations of motion are derived from a conservative Euler-Lagrange formulation with the non-dissipative forcing functions arising from steady, incompressible, inviscid 2 dimensional aerodynamics incorporating results from Thin Airfoil Theory. The resulting model predicts undamped, increasing oscillations below a critical airflow speed called the flutter bound-ary. The paper shows how this speed can be predicted from the eigenvalues of the system. By changing certain airfoil geometrical and mechanical prop-erties, it is demonstrated that it is possible to aeroelastically tailor the airfoil such that flutter is avoided for a given flight regime. The model adopted has been found deficient in its ability to predict a realistic flutter boundary. This problem is due to the absence of dissipative forces in the aerodynam-ics of the model. It has been suggested that the model can be made more realistic by incorporating unsteadiness into the aerodynamics of the system using results from Peters ’ finite state theory.