Nonlinear aeroelastic modeling and limit cycle oscillation characterization of full bridges through rational function approximation

This study presents a multimode coupled nonlinear flutter approach in terms of the rational function (RF) approximation technique and amplitude-dependent flutter derivatives, to address the underdevelopment of three-dimensional (3D) nonlinear flutter analysis for long-span suspension bridges. A high-order RF is invoked to characterize the 3D inhomogeneous distributed nonlinear self-excited forces resulting from spanwise variated flutter derivatives and multi-mode coupling. An iterative approach is utilized to determine the spanwise amplitude distributions under specific cycle steps, while a matrix optimization procedure is introduced to least squares identifying the coefficient set of the RF relevant to 3D aerodynamics. The frequency-independent complex eigenvalue method combined with cycle calculations is used to determine the 3D distributed modal characteristics as functions of wind speed and amplitude. By utilizing the existing double-layer iterative method along with a numerical example, the precision and robustness of the proposed method are validated from various perspectives, including flutter response, modal characteristics, spanwise limit cycle oscillation amplitude, and 3D nonlinear vibration characteristics. In conclusion, the method demonstrates good precision, robustness, and the ability to automatically search for multi-mode coupling characteristics and shows fewer limitations on the number of modes.