Flutter analysis and chaotic response of an airfoil accounting for structural nonlinearities

Airfoils with structural nonlinearities subject to two-dimensional subsonic flow may undergo aeroelastic instabilities even below the linear flutter boundary. This thesis studies the aeroelastic behaviour of airfoils accounting for structural nonlinearities. The feasibility and potential of a modern nonlinear dynamics approach to the understanding of the underlying dynamics is investigated.;Extensive numerical simulations were performed for a two-degree-of-freedom air-foil with a freeplay nonlinearity in the structural pitch moment and subject to two-dimensional incompressible inviscid flow. Different types of attractors were identified well below the linear flutter speed via numerical simulations of the system, and the existence of chaotic attractors was verified. Basins of attraction and bifurcation diagrams were constructed showing rather complex dynamics of the system below the divergent flutter boundary. In some cases physical explanations are given for the air-foil's behaviour. Effects of the airfoil and nonlinearity parameters, airfoil camber and angle of attack and the compressibility of the fluid on the results are also presented, and it is shown that the system response is very sensitive to many parameters.;Similar investigations are presented for an airfoil with either cubic, bilinear or hysteretic nonlinearities. In many cases, most notably where the airfoil is subject to small preload, small central stiffness and small hysteresis, chaotic motions are detected for a considerable range of speed. A period doubling route to chaos is obtained for the particular case of cubic nonlinearity.;Numerical simulations were also performed for an airfoil-aileron combination and an airfoil with active flutter control accounting for freeplay structural nonlinearities in the pitch or flap hinge moment. More complex dynamics and chaotic oscillations were obtained for these three-degree-of-freedom systems. For the case of a freeplay in the aileron hinge moment a quasi-periodic route to chaos was identified.;Various numerical methods were employed to solve the equations of motion. Similar results were obtained in terms of the bifurcations and the amplitude of oscillations for all the numerical methods, so verifying to some extent the different numerical methods employed.;The systematic investigation of the aeroelastic response of airfoils with structural nonlinearities showed the existence of complex dynamics, and for velocities well below the linear flutter boundary it was demonstrated that the motion can be stable or that the airfoil can oscillate in a periodic or chaotic manner. The aeroelastic response was shown to be highly dependent on the initial conditions and numerous airfoil, nonlinearity and flow parameters. The results suggest that for aeroelastic analyses of aerosurfaces a nonlinear investigation of precise models is necessary.