Bending aeroelastic instability of the structure of suspended cable-stayed beam

The new nonlinear partial differential equations (PDEs) model for the structure of suspended cable-stayed beam, which take into account the initial configuration of the main cable and the finite deformations of the structure, is proposed. The nonlinear ordinary differential equations, which describe the wind-induced bending vibrations of the structure at the first mode, are obtained by Galerkin method from the PDEs. In a parameter plane, which is spanned by the flow velocity and the stiffness coefficient of the cable stays, a Hopf bifurcation is researched through the normal form that is calculated using the multiple scale method. Around the double-Hopf bifurcation point, it is found that the vibration types may switch between the low-frequency, the high-frequency and the coupled modal vibration while the flow velocity or the stiffness coefficient is perturbed slightly. This indicates that deformations of the cable stays have significant influence on the bending aeroelastic instability of the structure.