多塔连跨悬索桥基频估算实用公式

Practical Formula of Fundamental Frequency Estimation for Multi-pylon Suspension Bridge

多塔连跨悬索桥的动力特性与中塔刚度、主跨数目等设计参数密切相关,而我国现有规范中的悬索桥基频估算公式是基于单跨悬索桥推导的,无法体现这些设计参数的影响,故不适用于多塔连跨悬索桥。基于能量原理,提出了多塔连跨悬索桥的竖弯和扭转自由振动基本方程,并通过修正振型基函数的Rayleigh法求解,得到了多塔连跨悬索桥的基频估算公式。考虑到工程实用性,通过量级分析略去了公式中的次要项,并对设计中难以获得的部分参数进行了近似处理,得到了多塔连跨悬索桥基频估算实用公式。最后给出了中塔刚度、主跨数、中塔约束条件、跨径等多个设计参数变化下的多塔连跨悬索桥算例。通过估算公式结果与有限元模型计算结果的对比表明,该基频估算实用公式有较高的精度,在多塔连跨悬索桥的初步设计阶段有较好的应用价值。

The dynamic characteristics of multi-pylon suspension bridge is highly related to the design parameters such as rigidity of mid-pylon and number of main span. Since the estimation formula of fundamental frequency in Chinese current specification was derived based on the ordinary suspension bridges, it is unavailable in estimating the fundamental frequency of multi-pylon suspension bridge without taking these design parameters into account. Based on the energy principle, the basic equations of vertical bending and torsional free vibration were established, then the estimation formula of fundamental frequency was obtained by solving the equations with Rayleigh method with modified basis founction. For engineering practicability concern, the estimation formula was simplified by ignoring some small terms in magnitude analysis and replacing some parameters which are difficult to get with approximate ones. Finally, the estimate results of several examples were given and compared to the results calculated by finite element method with respect to the variable design parameters including rigidity of mid-pylon, number of main span, constraint conditions at mid-pylon, and length of span, etc. It proves that the formulas have enough accuracy to utilize in preliminary design phase of multi-pylon suspension bridge, which shows that this formula has enough accuracy to be utilized in preliminary design phase of multi-pylon suspension bridge.