Abstract:

The dynamic behaviors of a wing structure incorporating both nonlinear and viscoelastic damping under extreme random loads are investigated, and the unrealistic white Gaussian noise assumption, which is an issue that leads to inaccurate designs for aircraft wings, is addressed. The extreme random loads are quantified by the colored Lévy noise, which possesses inherent heavy-tailed characteristic and temporal correlation, thereby enhancing the realism of the modeled load environment. A multi-scale method is adopted to derive the theoretical amplitude-frequency characteristics of the corresponding deterministic case. Subsequently, the effects of nonlinear damping, viscoelastic damping, and colored Lévy noise on the wing’s dynamics are studied. The results highlight the potential application of nonlinear damping in the design of vibration isolations for aircraft wing structures. In contrast to linear viscous damping, nonlinear damping effectively suppresses the resonance peaks of the airfoil system, while exponential viscoelastic damping increases these resonance peaks. Within the bistable region of amplitude-frequency response curves, we uncover that both the noise intensity and the correlation time of the colored Lévy noise can induce undesirable stochastic transitions. We reveal that a lower stability index, a higher noise intensity, or a shorter correlation time reduces the mean first passage time (MFPT) and raises the residence probability (RP), thereby elevating the likelihood of transitions. Notably, the colored noise causes a larger MFPT and a smaller RP than the white noise without temporal correlation, indicating a lower propensity for triggering the unexpected transitions. Compared with the colored Gaussian noise, the colored Lévy noise reduces the MFPT and raises the RP, owing to the presence of large jumps. Our findings provide a theoretical foundation for the safety design of aircraft wing structures operated under extreme conditions, enabling the effective avoidance of structural redundancy and the improvement of design margins.

Key words: airfoil system, nonlinear damping, colored Lévy noise, bistability, transition