Stability and Bifurcations of an Airfoil-Aileron Combination in Two-Dimensional Incompressible Inviscid Flow

Abstract

The objective of the present work is to obtain bifurcation diagrams of a three degreeof-freedom airfoil subjected to two-dimensional incompressible inviscid flow taking into account concentrated structural nonlinearities. The integro-dierenti al aeroelastic equations of motion for the three degree-of-freedom airfoil are reformulated into a system of eight first-order autonomous ordinary dierential equations. The eigenvalue analysis of the linearized equations clarifies the linear system behavior, and gives the linear flutter speeds. The nonlinear equations can be analyzed using numerous methods developed for autonomous ordinary dierential equations. In the present investigation, concentrated nonlinearities in the airfoil pitch or aileron hinge moments are considered and the equations are either integrated numerically using defect-controlled method or analyzed using collocation method. Fixed-points solutions are calculated analytically, and bifurcation diagrams showing both stable and unstable limit cycle oscillation are obtained numerically. The types of bifurcations are assessed by evaluating the Floquet multipliers. Results are also in agreement with those previously obtained via describing function and finite dierence methods.