Aeroelastic analysis and nonlinear characterization of three-degree-of-freedom systems with discontinuous nonlinearities

Abstract

The effects of freeplay, multi-segmented, and impact nonlinearities in the pitch and control surface degrees of freedom on the nonlinear responses of a three-degree of freedom aeroelastic system are investigated to characterize the nonlinear behavior and possible bifurcations. The system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom, a nonlinear torsional spring in the pitch degree of freedom, and a control surface with a nonlinear spring in the trailing edge. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Nonlinear characterization is performed to identify the system's response, under different representations of the nonlinear springs, below the linear flutter speed. The results show that grazing/sliding bifurcations are present and nonlinear coupling of the system's frequencies lead to complex responses including sudden transitions between harmonic and chaotic responses as the freestream velocity is increased. These responses, which include the sudden amplitude jumps, generation of higher harmonics and broadband oscillatory behavior, could result in catastrophic structural failures of aeroelastic systems even when operating below the linear flutter speed.