NUMERICAL ANALYSIS OF THE CABLE-BEAM-CABLE COUPLED EFFECT UNDER THE IN-PLANE MULTIPLE INTERNAL RESONANCES IN CABLE-STAYED BRIDGES

In cable-stayed bridges, the frequencies of adjacent cables’ local modes are close in value, resulting in the high probability of multiple internal resonances in the vertical plane. During the resonance, the coupled effect between cables transmitted by the beam, also named the coupled effect of cable-beam-cable, might intensify the cable’s vibration by changing the dynamic properties of the structure. To investigate the mechanism, considering the geometric non-linearity of the cable, a dynamic model, with eight cables and a variable-section beam, is established. The beam with multi-elastic supports in the model is reduced to a novel integrated dynamic system composed of discrete parametric lumped-mass beam segments. The dynamic equations of the model are obtained by the Galerkin method and amended by the difference methods. The modal properties of the model are solved by the eigenfunctions and verified by the finite element method. Moreover, the dynamic equations were numerically simulated by the 4th~5th-order Runge-Kutta method. The simulation results show that when the local modes of cables are “1∶1” coupled with different global modes, the vibration of cables are independent of each other, and the energy conversion only occurs between the resonant cable and the corresponding global mode. When multiple cables are simultaneously coupled to the global mode of a certain order, the phenomenon of multiple internal resonances can be observed in the model. The coupled effect of cable-beam-cable would affect the characteristics of resonated cables during the multiple resonances. Particularly, the coupled effect is mainly the excitation effect when coupled with the in-plane vertical global mode of the 7th-order. If the coupled effect was considered, the vibration amplitude of the cable would be excited to nearly twice that of the single internal resonance. Additionally, the coupled effect is inversely correlated with the distance between the cables and is positively correlated with the cable mass and the amplitude corresponding to vibration mode at the anchored position.