A continuation method for determining the speed dependent modal properties of large MDOF aeroelastic systems

Abstract

In this article, an arc-length continuation process is presented as an alternative to the classical p-k method to determine the pre-flutter modal properties of an aeroelastic system. The algorithm is based on a reformulation of the generalized eigenvalue problem into a set of nonhomogeneous algebraic equations and on the addition of a continuation equation. The reformulated system is then solved with several nonlinear solvers, and the performance of the resulting algorithms is compared to that of the p-k method on three examples. The analysis is performed mode-by-mode, initiated from wind-off conditions and gradually progressing until aeroelastic instability. The research findings highlight the efficiency of continuation methods, thanks to their ability to refine the wind speed mesh where the system experiences local variations related to rapid aeroelastic changes. The various versions of the proposed algorithm show faster convergence than the direct approach, but also excellent stability performance even in critical regimes. Finally, the mode-by-mode solution allows the use of a custom wind speed mesh for each mode separately and prevents mode swapping.