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.

在悬索桥的设计和分析中，通常将主缆视为仅传递拉力的软缆。新铁路中使用的大跨度悬索桥要求将主缆线设计为具有较大的横截面和较高的弯曲刚度。后者会影响整个桥梁的动态行为。为此，在考虑静载荷作用下的弯曲刚度的前提下，建立了主电缆形状的解析表达式。根据D'Alembert原理，推导并求解了悬索桥中电缆振动的偏微分方程。最后，考虑主电缆的弯曲刚度，计算桥梁弯曲和扭转振动的频率和模式形状。为了验证该方法的可行性，以五峰山长江大桥为例进行了研究。将分析结果与ANSYS软件获得的有限元解决方案进行了比较，取得了很好的一致性。通过提出的方法，分析了主缆弯曲刚度对悬索桥弯曲和扭转振动的影响。结果表明，电缆的弯曲刚度对弯曲振动的影响大于扭转振动。随着电缆弯曲刚度的增加，桥的频率变得更高。此外，随着振动模式的阶数或电缆与梁的抗弯刚度之比的增加，主电缆抗弯刚度的影响也越来越大。将分析结果与ANSYS软件获得的有限元解决方案进行了比较，取得了很好的一致性。通过提出的方法，分析了主缆弯曲刚度对悬索桥弯曲和扭转振动的影响。结果表明，电缆的弯曲刚度对弯曲振动的影响大于扭转振动。随着电缆弯曲刚度的增加，桥的频率变得更高。此外，随着振动模式的阶数或电缆与梁的抗弯刚度之比的增加，主电缆抗弯刚度的影响也越来越大。将分析结果与ANSYS软件获得的有限元解决方案进行了比较，取得了很好的一致性。通过提出的方法，分析了主缆弯曲刚度对悬索桥弯曲和扭转振动的影响。结果表明，电缆的弯曲刚度对弯曲振动的影响大于扭转振动。随着电缆弯曲刚度的增加，桥的频率变得更高。此外，随着振动模式的阶数或电缆与梁的抗弯刚度之比的增加，主电缆抗弯刚度的影响也越来越大。分析了主缆弯曲刚度对悬索桥弯曲和扭转振动的影响。结果表明，电缆的弯曲刚度对弯曲振动的影响大于扭转振动。随着电缆弯曲刚度的增加，桥的频率变得更高。此外，随着振动模式的阶数或电缆与梁的抗弯刚度之比的增加，主电缆抗弯刚度的影响也越来越大。分析了主缆弯曲刚度对悬索桥弯曲和扭转振动的影响。结果表明，电缆的弯曲刚度对弯曲振动的影响大于扭转振动。随着电缆弯曲刚度的增加，桥的频率变得更高。此外，随着振动模式的阶数或电缆与梁的抗弯刚度之比的增加，主电缆抗弯刚度的影响也越来越大。