Published: May 24, 2025 by Daning Huang
The Koopman theory is now a well-known tool in the analysis of nonlinear dynamics. Our work looks into how Koopman theory, particularly the Koopman Bilinear Form (KBF) and its extension (EKBF), can be leveraged in the global linear representation of aeroelastic dynamics, including Hopf bifurcation with flutter behaviors.
The effectiveness of the proposed methodology is demonstrated through two case studies: a 2D academic example and a panel flutter problem. Results show that EKBF effectively interpolates and extrapolates principal eigenvalues, capturing flutter mechanisms, and accurately predicting the flutter boundary even when the data is corrupted by noise. Furthermore, parameterized isostable and isochron identified by EKBF provides valuable insights into the nonlinear flutter system.
