变截面桥墩复合振动基频近似算法

为了快速准确地估算出桥墩的振动基频,在瑞利法和Southwell频率合成法的基础上导出了变截面桥墩复合振动基频的计算公式.将基频表示成各惯性元和复原元所组成子系统的频率合成,其中惯性元为墩身分布质量和墩顶集中质量;复原元包括基础变形、墩身弯曲和剪切变形.然后用有限元建模来验证该方法,并分析了不同变截面系数和墩顶附加质量比对桥墩基频的影响.计算结果表明,导出的公式与有限元计算结果很接近.该方法适用于各种基础类型的桥墩和高耸结构基频的估算.

Approximate algorithm of compound fundamental frequencies of tapered bridge piers

A simple, accurate and flexible formula to calculate the fundamental frequencies of tapered bridge piers is presented. The approach was developed based on the combination of Rayleigh and Southwell methods. The fundamental frequency of a pier was decomposed to the sum of frequency of each subsystem consisted in inertia component and deformable component. The inertia component includes distributed mass of pier and concentrated mass on its top while deformation component includes deformation of foundation, flexural deformation and shear deformation. Then finite element analysis (FEA) was used to establish models to verify the presented approach. The influence of different taper ratios and mass ratios of the top of a pier on fundamental frequency is also discussed. The results from these two approaches are in close agreement. The formula presented in this paper is adaptable to calculate fundamental frequencies of bridge piers and all kinds of tower structures.