CALCULATION OF FLUTTER DERIVATIVES AND SPEED FOR 2-D INCOMPRESSIBLE-FLOW BY THE FINITE-ELEMENT METHOD

A general linear superposition theory for finite-element formulation is proposed for airfoil pitching, heaving, and control surface oscillations. It divides the solution into time-independent and the first-harmonic subsolutions. The crucial part of the formulation is the finite-element treatment of the wake behind the trailing edge, which is modelled through velocity potential difference rather than the conventional tangential velocity difference. The proper numerical form of the unsteady Kutta condition is discussed in detail. To avoid any numerical blockage effect, a parametric study of finite-element mesh sizes is also conducted. finally, the unsteady aerodynamic forces obtained are employed to calculate flutter speed with a new iteration scheme. Both the unsteady aerodynamic forces and the flutter speed are compared with either numerical or know theoretical solutions. The agreement is good.