Nonlinear vibration of the coupled structure of suspended-cable-stayed beam—1:2 internal resonance

Through the Galerkin method the nonlinear ordinary differential equations (ODEs) in time are obtained from the nonlinear partial differential equations (PDEs) to describe the motion of the coupled structure of a suspended-cable-stayed beam. In the PDEs, the curvature of main cables and the deformation of cable stays are taken into account. The dynamics of the structure is investigated based on the ODEs when the structure is subjected to a harmonic excitation in the presence of both high-frequency principle resonance and 1:2 internal resonance. It is found that there are typical jumps and saturation phenomena of the vibration amplitude in the structure. And the structure may present quasi-periodic vibration or chaos, if the stiffness of the cable stays membrane and frequency of external excitation are disturbed.