Derivation of ordinary differential equations for a 3-DOF airfoil-aileron combination subjected to unsteady incompressible flow

Abstract

This paper presents a set of ordinary differential equations (ODEs) for the dynamics of a three degree-of-freedom (3-DOF) airfoil-aileron combination subjected to unsteady incompressible inviscid flow. Integro-differential equations of motion for the 3-DOF aeroelastic system are reformulated into a set of eight first-order autonomous ODEs. These are the simplest and least number of ODEs that can present this aeroelastic system.The new set of equations can be analyzed using numerous analytical and numerical methods, which have been developed for autonomous ODEs. In the present work, the linear system behavior and the linear flutter speed are simply evaluated through the eigenvalue analysis of the ODEs. Concentrated structural nonlinearities are then considered in the airfoil pitch and aileron hinge moments. The nonlinear equations are either integrated numerically using a defect-controlled method or analyzed using collocation method. Sample bifurcation diagrams are presented here for the nonlinear system.