Multimode coupled nonlinear flutter analysis for long-span bridges by considering dependence of flutter derivatives on vibration amplitude

This study presents a multimode coupled nonlinear flutter analysis method for long-span bridges with consideration of vibration-amplitude-dependent flutter derivatives. By converting the equation of motion into a complex eigenvalue problem, a double layer iterative method (DLIM) is proposed to determine the real iterative frequency as well as the participation of each structural mode shape to the flutter response for a given wind speed and vibration amplitude. The accuracy of the proposed scheme is cross-validated with a classical bimodal analysis method. Two suspension bridges, characterized by a soft type and a hard type nonlinear flutter, respectively, are used to examine the performance of the proposed method. Modal properties (i.e., damping ratio and frequency), as functions of wind speed and vibration amplitude, can be estimated such that the nonlinear flutter response including the critical wind speed and vibration amplitude can be accurately quantified. At last, the coupling effect among different structural modes and its further influence on the genesis and evolution of the nonlinear flutter are also discussed.