Effect of the main cable bending stiffness on flexural and torsional vibrations of suspension bridges: Analytical approach

Abstract

In the design and analysis of suspension bridges, the main cables are conventionally treated as flexible ropes transmitting only tensile loads. Large-span suspension bridges used in new railways require the main cables to be designed with larger cross-sections and higher bending stiffness. The latter can affect the dynamic behavior of the entire bridge. To this end, the analytical expression of the main cable's shape is established in this paper, considering the bending stiffness under the dead loads. According to the D'Alembert principle, the partial differential equations of vibration of the cable in the suspension bridge are derived and solved. Finally, frequencies and mode shapes of the flexural and torsional vibrations of the bridge are calculated considering the main cable bending stiffness. To verify the feasibility of the proposed method, a case study of the Wufengshan Yangtze River Bridge is investigated. The analytical results are compared with the finite element solutions obtained by the ANSYS software, with good agreement achieved. By using the proposed method, the effect of the main cable bending stiffness on the flexural and torsional vibrations of suspension bridges is analyzed. The results show that the cable bending stiffness has a larger effect on flexural vibrations than torsional vibrations. The bridge's frequencies become higher with the increase of cable bending stiffness. Besides, as the order of vibration mode or the ratio of the bending stiffness of cables to the beam increases, the effect of main cable bending stiffness gets greater.