### Vortex-Induced Vertical Vibrations of Suspension Bridges

Alexander N. Blekherman
2013 Proceedings of the Eighth Asia-Pacific Conference on Wind Engineering   unpublished
The possibility of large oscillations of a bridge deck caused by cross winds of relatively low speed is one of the problems in dynamics of suspension bridges. The abovementioned phenomenon is treated as vortex-induced oscillations. The purpose of this paper was to develop a semi-empirical mathematical model describing the dynamic behavior of the suspension bridge and determination of its maximum amplitude at vertical vibrations caused by vortex shedding. Taking into account the need to account
more » ... he need to account for the interaction between the flow of wind and streamlined bridge, the model was developed on the basis of a combination of two approaches: the analysis of dynamics of a suspension bridge (a linear model) under external uniformly distributed along the bridge harmonic vertical load * and the Hartlen & Currie model describing the interaction between a smooth flow and streamlined cylinder where the latter can strongly affect the lift force. Based on the joint consideration of both approaches, the extended Hartlen & Currie model was obtained to describe the behavior of the suspension bridge under the condition of vortex shedding. This model permits two regimes of self-exciting vibrations. One of them is the case, when the ratio between a Strouhal's frequency and one of the natural frequencies corresponding with the vertical mode of the bridge is close to 1:1, and another, when the same ratio is close to 2:1. Thus, the suspension bridge can have two critical speeds for each of its natural frequency. In accordance with the proposed model, if a higher speed is achievable, then the full aeroelastic model of the bridge should be tested in a smooth flow, although usually a sectional model for testing is considered as valid one. The response of a nonlinear two degree-of-freedom system was investigated. The perturbation method of multiple time scales was used to construct first-order nonlinear differential equations and to determine steady state solutions and their stability. The bifurcation diagrams were plotted for both cases. Suppressing of undesirable vibrations of the bridge deck was discussed. Numerical calculations showed that decreasing the lift force by installing fairings or increasing damping of the suspension bridge or their combination could decrease vertical self-excited vibrations or even prevent their arising.