Abstract
The paper treats the question of the existence of limit cycle oscillations and domain of stability (attraction) of prototypical aeroelastic wing sections with pitch structural nonlinearity using the describing function method. The model includes unsteady aerodynamics based on Theodorsen’s theory. The dual-input describing functions of the nonlinearity are used for the limit cycle analysis. Analytical expressions for the computation of the average value, and the amplitude and frequency of oscillation of pitch and plunge responses are obtained. Interestingly, it is found that flutter can exist not only when the origin in the state space is unstable but also when it is asymptotically stable if the initial conditions are not small. For such cases, an estimate of the domain of stability surrounding the origin in the state space is computed in which flutter cannot exist. The Nyquist criterion is used to establish the stability of the limit cycle and it is shown that unstable as well as the stable limit cycles exist when the origin is exponentially stable. Numerical results are presented for a set of values of the flow velocities and the locations of the elastic axis which show that the predicted limit cycle oscillation amplitude and frequency as well as the mean value are quite close to the actual values.
Published Version
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