The vortex-excited vibrations of coupled structure of cable-stayed beam

In this paper the new non-linear partial differential equations is established. This new modal describes the vortex-excited vibrations of coupled structure of cable-stayed beam in vertical plane. The partial differential equations are transformed into ordinary differential on time domain equations by Galerkin method. The first approximate solutions of the ordinary differential equations are obtained by the multiple scales method when vortex-excited frequency close to frequencies of natural structure. The analyses results indicates that the structure contains two frequencies for jth normal mode of the structure. When the vortex frequency close to natural frequency of the structure the amplitude of structure increase suddenly. This vortex-excited vibration phenomenon is observed in the Tacoma Narrows bridge. The first approximation solutions and analysis method in this paper provide a convenient checking method for a practical coupled structure of cable-stayed beam.