Nonlinear Free Vibrations of Suspension Bridges: Application

The basic characteristics of the nonlinear free flexural‐torsional vibrations of two suspension bridges are examined. The Golden Gate Bridge and the Vincent‐Thomas Bridge were chosen to represent both a relatively long‐and a relatively short‐span suspension bridge's vibrations. The amplitude‐frequency relationships of the first six modes (symmetric and antisymmetric) of both vertical and torsional vibrations for each bridge are presented. The case when one of the linear natural frequencies of vertical vibration is equal to, or approximately equal to, another linear natural frequency of torsional vibration, is considered. This case revealed that the two modes are strongly coupled. Finally, a comparison between the analytical results obtained via the perturbation analysis and those obtained by the numerical integration of the governing coupled nonlinear equations of motion is presented. The agreement is reasonably good.