The Aeroelastic Response of a 3-DOF Airfoil with Structural Nonlinearities
by
Hekmat Alighanbari
Ryerson Polytechnic University

A two-dimensional airfoil-flap combination with freeplay structural nonlinearities in pitch and flap, and subject to incompressible flow has been analyzed. Aerodynamic forces for arbitrary motions of a 3-DOF airfoil are derived from Theodorsen's equations using Wagner's function. The resulting equations of motion are either integrated numerically using a finite difference method, or solved in a semi-analytical manner using dual-input describing function technique. The flutter analysis of the airfoil with a nonlinearity in the flap hinge moment indicates limit cycle, quasi-periodic and chaotic oscillations for velocities well below the linear flutter boundary. The basin of attraction obtained for the system shows that the existence of the different types of motion is highly dependent on the air-speed and initial conditions. For the airfoil with nonlinear pitch and flap hinge moments large regions of limit cycle and chaotic oscillations are detected.

Numerical simulation has also been conducted for the airfoil with active flutter control accounting for the nonlinearities. The trailing-edge flap with a localized damping type transfer function is employed to suppress the flutter. It is shown that the control system is able to increase the linear flutter boundary and damp out the oscillations below the violent flutter speed; however, the airfoil's stable positions could be at nonzero pitch angles.

Date received: January 14, 2000