Flutter analysis of an airfoil with bounded random parameters in incompressible flow via Gegenbauer polynomial approximation

The effects of parameter uncertainty on the flutter characteristics of a two-dimensional airfoil in an incompressible flow were investigated through Gegenbauer polynomial approximation. The uncertain parameters, such as the linear and cubic pitch stiffness coefficients are modeled as bounded random variables with λ-PDFs (probability density functions). With the aid of Gegenbauer polynomial approximation, the two-dimensional stochastic airfoil system is transformed at first into its equivalent deterministic one. Then the Hopf-bifurcation point is determined through the equivalent deterministic system, and the onset of the flutter, together with the flutter frequency against the probability density distribution parameter and the intensity of the random variable is explored. In addition, the ranges of the peak pitch and plunge responses against the flight speed and the PDFs of the peak pitch response are obtained. Numerical results show how the probability density distribution parameters and the intensities of random parameters affect the flutter onset speed, flutter angular frequency, the upper and lower boundaries of peak responses, and the PDFs of peak responses.