Flutter-Margin Method Accounting for Modal Parameters Uncertainties

Abstract

The flutter margin method developed by Zimmerman and Weissenburger in 1964 is a useful tool to extrapolate the flutter speed from in-flight measured frequency and decay data at preflutter airspeeds. The usefulness of the method is based on reliable and accurate modal parameter estimations, which, in reality, can exhibit a nonnegligible amount of scatter. In this paper, Zimmerman and Weissenburger’s method is extended to capture more effectively the inherent uncertainty present in the test data. Two approaches are proposed such that all “good” measured values of the modal parameters are used to construct either flutter margin or flutter speed histograms. Probabilitydensity-function (PDF) models are also developed. It is found that the flutter margin and flutter speed pdfs are not symmetrical and right skewed with mean > median > mode. Furthermore, the flutter margin follows a gamma distribution. Different flutter margin and flutter speed statistics are investigated. Related to the flutter-margin pdf, the mode is considered to be the most relevant estimate of the flutter margin; use of the mode as the appropriate central statistic addresses the uncertainty by giving a more conservative flutter-margin estimate. With regard to the pdf of the flutter speed, consistent and conservative flutter speed predictions are obtained for any of the chosen central statistics. The two approaches are evaluated on the basis of real F-18 flight data and of simulated data.