Stochastic Flutter Analysis

The field of fluid-structure interaction is combined with the field of stochastics to perform a stochastic flutter analysis. Various methods to directly incorporate the effects of uncertainties in the flutter analysis are investigated. The panel problem with a supersonic fluid flowing over it is considered as a testcase. The stochastic moments (mean, standard deviation, etc.) of the flutter point are computed by an uncertainty analysis. Sensitivity-based methods are used to determine the stochastic moments of the flutter point. This is done by implicit differentiation of the flutter requirement. The moments can also be determined using the spectral method, which can be considered as a projection method. An iterative solution to the general random eigenvalue problem is proposed for determining the spectral expansion of the flutter point. It turns out that the asymptotic method, which is a sensitivity-based method, is the most efficient method for approximating the moments of the flutter point. The success of this method can be explained by the fact that the relation between the random Mach number and the random field of elastic properties is close to linear. The probability of the occurrence of flutter below a specified Mach number can be computed using a reliability analysis. Fully sampling-based techniques are not applicable, since the required sample size would be to large. The probability of failure can be approximated without the use of sampling by the use of the first- and second-order reliability method. The results of these methods are inaccurate however. The importance sampling method combines the speed of the reliability methods with the accuracy of the sampling techniques to obtain an efficient approximation of the probability of flutter