Nonlinear Analysis and Identification of Limit Cycle Oscillations in an Aeroelastic System

The identi cation of a concentrated nonlinearity in the torsional spring of an aeroelastic system is performed. The system consists of a rigid airfoil that is supported by a linear spring in the plunge motion and a nonlinear spring in the pitch motion. Quadratic and cubic nonlinearities in the pitch moment are introduced to model the concentrated nonlinearity. The aerodynamic loads are modeled using two di erent representations, namely, the quasi-steady approximation and the Duhamel formulation. Unlike the quasi-steady approximation which fails to correctly predict the utter speed, the Duhamel formulation yielded accurate prediction for the utter speed and frequency. The results show that the use of the Duhamel formulation to represent the aerodynamic loads yields excellent agreement between the experimental data and the numerical predictions.