Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

Abstract

The effects of a multi-segmented nonlinearity in the pitch degree of freedom on the behavior of a two-degree of freedom aeroelastic system are investigated. The aeroelastic system is free to plunge and pitch and is supported by linear translational and nonlinear torsional springs and is subjected to an incoming flow. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Using modern method of nonlinear dynamics, a nonlinear characterization is performed to identify the system's response when increasing the wind speed. It is demonstrated that four sudden transitions take place with a change in the system's response. It is shown that, in the first transition, the system's response changes from simply periodic (only main oscillating frequency) to two periods (having the main oscillating frequency and its superharmonic of order 2). In the second transition, the response of the system changes from two periods (having the main oscillating frequency and its superharmonic of order 2) to a period-1. The results also show that the third transition is accompanied by a change in the system's response from simply periodic to two periods (having the main oscillating frequency and its superharmonic of order 3). After this transition, chaotic responses take place and then the fourth transition is accompanied by a sudden change in the system's response from chaotic to two periods (having the main oscillating frequency and its superharmonic of order 3). The results show that these transitions are caused by the tangential contact between the trajectory and the multi-segmented nonlinearity boundaries and with a zero-pitch speed incidence. This observation is associated with the definition of grazing bifurcation. Published by Elsevier B.V.