MODELLING AND ANALYSIS OF THE IN-PLANE DYNAMICS OF CABLE-STAYED BRIDGES CONSIDERING THE PYLON-CABLE-BEAM COUPLING EFFECT

To study the pylon-beam modal coupling effect on the global modes and 1:1 internal resonance of rigid-frame cable-stayed bridges, a novel in-plane dynamic model, considering the geometric nonlinearity caused by cables’ initial sag and lateral large displacement, is established in this paper. The bridge pylon and beam in the model are modelled as integrated systems consisting of discretized parametric segments. The dynamic equations of the whole structure are derived based on the dynamic connections between the pylon-cable, cable-beam, and pylon-beam nodes. Using the finite difference method, the dynamic balance differential equations of the parametric system are transformed algebraically. The whole bridge governing equations and modal functions are obtained through the modal drag method and variable separation method. Based on the simulation of the undamped equations via Runge-Kutta method of 4 ~ 5-order, the modal veering phenomena between local-global modes and dominant-nondominant modes are observed. The simulation results shows that pylon-beam modal interaction has no significant effect on the low-order symmetric and high-order global modes of the structure, for which completely dominated by the local modes of the pylon or beam is complete global mode. Moreover, it is obtained that the local modes of the pylon or beam have a significant effect on the low-order anti-symmetric global modes, for which jointly dominated by both pylon and beam modes is hybrid global modes. It is verified that the coupling 1:1 internal resonance is excited when the local modal frequency of the cable meets both types of global modes. The localized factor of each component in the global modes plays an important factor in measuring the degree of internal resonance participation. In a complete global mode internal resonance, non-dominant modes do not participate in the internal resonance of the structure, and energy conversion occurs only between the dominant component mode and the cable local mode. In a hybrid global mode internal resonance, non-dominant modes participate in internal resonance and would change the dynamic characteristics of the cable vibration response. The influence varies with the order of global modes and cable mechanical parameters.