Investigations on the interactions between structural and aerodynamic nonlinearities and unsteadiness for aeroelastic systems
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A nonlinear analysis is performed on a two-degree-of-freedom wing-based system. Structural nonlinearities are introduced in the pitch degree of freedom when considering two different forms of the aerodynamic loads. Comparisons between quasi-steady and unsteady aerodynamic representations are investigated and discussed including stall effects. The nonlinear aeroelastic response is carried out in the presence of quadratic and cubic nonlinearities in the pitch degree of freedom. The effects of the stall and unsteadiness of the flow on the type of Hopf bifurcation and the limit cycle oscillations of the system are investigated. A comparative study between the unsteady and quasi-steady representations from a nonlinear perspective is also carried out. Results from the linear analysis show that for this specific aeroelastic system, the effect of the noncirculatory terms on its linear characteristics is dependent on the aerodynamic representation and the system’s design. Additionally, the quasi-steady approximation of the aerodynamic loads results in an inaccurate prediction of the linear flutter speed. On the other hand, the nonlinear analysis shows the existence of an instability shift from the supercritical to the subcritical type, depending on the value of the stall coefficient, as well as that of the cubic and quadratic nonlinearities, more dominantly for the case when the quasi-steady representation is used to approximate the aerodynamic loads. The results show that, even for small, reduced frequencies and small angles of attack scenarios, the unsteady representation of aerodynamic loads is critical to correctly predict the flutter speed, instability type, and system’s dynamics.