Propagation of structural uncertainty to linear aeroelastic stability

Abstract

The problem of linear flutter analysis in the presence of structural uncertainty is addressed. Whereas the propagation of uncertain structural parameters in finite element models has been carried out by a number of different methods, there appears to be less published work on the influence of random structural parameters on flutter speed. In this paper, we first evaluate the sensitivity of aeroelastic damping to a number of uncertain structural, geometrical and structural-damping parameters. The most significant parameters are identified and then randomised. Secondly, interval, fuzzy and probabilistic methods are used to propagate the structural uncertainty through the aeroelastic analysis resulting in regions of flutter-boundary uncertainty characterised by intervals, fuzzy membership functions and probability density functions. Interval analysis requires two optimisation procedures in order to find the bounds of the aeroelastic responses. The Response Surface Method (RSM) permits efficient optimisation and is used for the estimation of the gradient and Hessian. The resulting intervals are checked using Monte-Carlo Simulation (MCS). Probabilistic analysis is carried out using both first- and second-order perturbation, using the gradient and the Hessian determined by RSM. The first-order perturbation method is generally found to produce results in good agreement with the MCS, although there are differences at the tails of the distributions, especially for the unstable modes close to the flutter speed. The second-order perturbation method provides an improved prediction of the nonlinear behaviour at the tails. The flutter membership function predicted by the fuzzy method generally includes the nonlinear behaviour at the tails of the MCS distribution. Variability in structural mass and stiffness parameters is shown to have a significant effect upon the flutter intervals. Structural damping results in a small but significant increase in the flutter speed, but structural-damping variability does not translate into significant intervals of flutter-boundary uncertainty. Studies are carried out on the Goland wing, with and without structural damping, and on a generic fighter model.