计入主塔刚度影响的三跨连续体系悬索桥竖弯频率估算公式

为方便计算三跨连续体系悬索桥的竖向自振频率，基于双塔三跨连续体系悬索桥，在计入主塔刚度的影响下，应用Rayleigh法，推导了一阶对称和反对称竖弯振动频率公式，并提出了主塔刚度影响系数的表达式，最后，对此公式的可行性进行了算例验证，并对适用范围进行了讨论。研究结果表明：主塔刚度对三跨连续体系的一阶正对称竖弯频率影响较大，进行频率计算时应计入主塔刚度的影响；主塔对竖弯基频的影响程度可通过主塔刚度影响系数计算得到；给出的能量法得到的竖弯基频计算值与有限元值误差能满足概念设计阶段的要求；该公式可用于简支单跨及三跨连续体系悬索桥的竖弯基频计算中。

Estimation Frequency Formulas for Vertical Vibration for Three-span Continuous System Suspension Bridge Considering Tower Stiffness Influence

To calculate vertical frequency of three-span continuous system suspension bridge conveniently, the three-span continuous system suspension bridge with double-towers was taken as research object. Frequency formulas for first symmetric and asymmetric vertical vibration modes were deduced by the Rayleigh method considering tower stiffness influence, and the influence coefficient of tower stiffness was proposed. Finally, the proposed formulas were validated by the engineering project, and the application condition was discussed. The results indicate that tower stiffness has a great influence on first symmetric vertical frequency, which should be considered in frequency calculation. The extent of influence can be assessed by the main tower stiffness coefficients formula. The error between values calculated by the proposed formula and the finite element method ( FEM ) satisfy the requirement of conceptual design. The proposed formulas can be applied to the simple-supported single or three-span continuous suspension bridge.