A novel analytical method for multi-modal coupled flutter in turbulence based on moment Lyapunov exponent

The moment Lyapunov exponent in stochastic stability theory serves as a critical metric for investigating flutter stability in turbulence. However, theoretical analysis of the moment Lyapunov exponent remains confined to two-degree-of-freedom aeroelastic systems. For stochastic stability problems involving multi-modal coupling effects, current research still necessitates reliance on the Monte Carlo simulation, an extremely time-consuming approach, to determine the moment Lyapunov exponent. Multi-modal coupling effects and the unsteady characteristic of aerodynamic self-excited forces in flutter of flexible structures, such as long-span bridges, prove non-negligible. Theoretical expressions for the moment Lyapunov exponent of multi-modal coupled aeroelastic systems in turbulence remain unestablished in contemporary stochastic stability theory. This paper presents, for the first time, the asymptotic expansion for the moment Lyapunov exponent of the multi-modal coupled flutter system incorporating unsteady aerodynamic forces. Based on the asymptotic expansion, a novel analytical method is proposed for assessing the flutter stability of multi-modal coupled aeroelastic systems in turbulence. The proposed method is validated through a finite element model case study of a long-span suspension bridge. The numerical results demonstrate that the proposed method achieves comparable accuracy to Monte Carlo simulations in determining the moment Lyapunov exponents for a high-dimensional stochastic dynamic system of multi-modal coupled flutter, with computational efficiency improved by four orders of magnitude. This study proposes an accurate and efficient computational method for multi-modal coupled flutter analysis of aeroelastic systems in turbulence while establishing a transferable framework for determining the moment Lyapunov exponent in high-dimensional stochastic dynamic systems.