Inverse stochastic resonance in a two-dimensional airfoil system with nonlinear pitching stiffness driven by Lévy noise.

Abstract

The aircraft can experience complex environments during the flight. For the random actions, the traditional Gaussian white noise assumption may not be sufficient to depict the realistic stochastic loads on the wing structures. Considering fluctuations with extreme conditions, Lévy noise is a better candidate describing the stochastic dynamical behaviors on the airfoil models. In this paper, we investigated a classical two-dimensional airfoil model with the nonlinear pitching stiffness subjected to the Lévy noise. For the deterministic case, the nonlinear stiffness coefficients reshape the bistable region, which influences the size of the large limit cycle oscillations before the flutter speed. The introduction of the additive Lévy noise can induce significant inverse stochastic resonance phenomena when the basin of attraction of the stable limit cycle is much smaller than that of the stable fixed point. The distribution parameters of the Lévy noise exhibit distinct impacts on the inverse stochastic resonance curves. Our results may shed some light on the design and control process of the airfoil models.