Improved understanding of bimodal coupled bridge flutter based on closed-form solutions

Analysis of an aeroelastic bridge system consisting of the fundamental vertical and torsional modes of vibration offers an expeditious assessment of bridge flutter performance. It also produces valuable insight into the multimode coupled bridge response to strong winds. This paper presents closed-form formulations for estimating the modal frequencies, damping ratios, and coupled motions of the bimodal coupled aeroelastic bridge system at varying wind velocities. The derivation of these formulations is based on the assumption of low-level damping of the aeroelastic bridge system. This assumption has also been adopted in current modeling of self-excited forces and the analysis of coupled flutter through complex eigenvalue analysis. This framework leads to a formula for determining the critical flutter velocity of bridges with generic bluff deck sections, which not only provides an analytical basis for Selberg's empirical formula, but also serves as its extension to generic bridges. This formula gives a single parameter or index as a function of flutter derivatives to describe the flutter efficiency of a given bridge section, which facilitates comparison of aerodynamic characteristics of different bridge deck sections. The accuracy of the proposed framework is illustrated through long span bridge examples with a variety of structural and aerodynamic characteristics. Based on the proposed framework, the significance of structural and aerodynamic characteristics on the development of coupled motion and the evolution of modal damping is discussed, which helps to better understand how and where bridges may be tailored for better flutter performance. It is pointed out that coupled bridge flutter is initiated from the modal branch that has a higher modal frequency and is characterized by coupled motion in which torsional motion lags vertical motion. The generation of coupled flutter instability is driven by the negative damping effect caused by the coupled self-excited forces.