Derivation of ODEs and Bifurcation Analysis of a Two‐DOF Airfoil Subjected to Unsteady Incompressible Flow

An airfoil subjected to two-dimensional incompressible inviscid flow is considered.The airfoil is supported via a translational and a torsional springs. The aeroelasticintegro-differential equations of motion for the airfoil are reformulated into a system ofsix first-order autonomous ordinary differential equations. These are the simplest andleast number of ODEs that can present this aeroelastic system. The differential equations are then used for the bifurcation analysis of an airfoil with a structural nonlinearity in the pitch direction. Sample bifurcation diagramsshowing both stable and unstable limit cycle oscillation are presented. The types ofbifurcations are assessed by evaluating the Floquet multipliers. For a specific case, aperiod doubling route to chaos was detected, and mildly chaotic behavior in a narrowrange of velocity was confirmed via the calculation of the Lyapunov exponents