An asymptotic expansion of the moment Lyapunov exponent for flutter instability in turbulence with emphasis on unsteady forces

The moment Lyapunov exponent of stochastic stability theory serves as an effective approach for investigating flutter instability in turbulence. Unlike the aerodynamic self-excited forces acting on airfoils, the aerodynamic self-excited forces on bridges exhibit significantly more pronounced unsteady characteristics. Due to the complexity of these unsteady forces, existing research has predominantly relied on Monte Carlo simulations to estimate the moment Lyapunov exponent on flutter instability, and theoretical expressions for moment Lyapunov exponent of modal coupled flutter driven by wide-band noise remain unestablished. This study derives, for the first time, an asymptotic expansion of the moment Lyapunov exponent for the bimodal coupled flutter driven by unsteady forces in turbulent flow. Our method involves integrating state-space equations, a generalized stochastic turbulence model, the modified stochastic averaging method, the Girsanov theorem, the Feynman-Kac formula, and the Fourier cosine series expansion. Our work extends the existing asymptotic expansion of the moment Lyapunov exponent from quasi-steady to unsteady aeroelastic systems, thereby addressing the critical theoretical gap in this area. Furthermore, the derived asymptotic expansion is validated through Monte Carlo simulations. This study establishes connections between mathematical models and engineering applications by employing a simplified engineering case, providing profound insights for the implementation of the moment Lyapunov exponent in practical engineering applications. Moreover, this study offers a transferable mathematical framework for the theoretical derivation of the moment Lyapunov exponent in high-dimensional stochastic systems driven by wide-band noise.