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Transfer matrix method of in-plane eigenvalues during cantilever construction of arch bridge

DOI：10.7511/jslx20210101002

 作者 单位 E-mail 康厚军 湖南大学 土木工程学院, 长沙 410082广西大学 土木建筑工程学院, 南宁 530004 khjun@hnu.edu.cn 朱国敬 湖南大学 土木工程学院, 长沙 410082 苏潇阳 湖南大学 土木工程学院, 长沙 410082

采用传递矩阵法对拱桥悬臂施工过程中的面内特征值问题进行求解,建立了该类桥型施工过程中面内竖弯刚度的评估方法。首先,将索和拱分别视为无垂度的张紧弦和欧拉伯努利梁,基于传递矩阵法基本理论推导了系统的总传递矩阵,考虑拱和索的边界条件以及索拱节点的位移连续性条件得到系统的特征值方程,进而计算出系统的频率和模态。同时,采用有限元分析软件ANSYS15.0建立拱桥合拢状态的有限元模型并得到频率和振型的有限元解,通过对比本文方法与有限元方法计算结果,证明本文方法和模型的正确性。然后,分别采用上述理论方法和有限元方法对拱桥合拢前半跨模型的频率和模态进行分析对比,两者结果一致进一步说明了本文方法和模型的正确性。最后,选取了索的弹性模量、初始索力以及拱桥的半径等参数,作为考虑影响结构自振频率的因素,对模型的前六阶频率进行了系统的参数分析,得出拱桥的设计参数以及合拢状态下索的设计参数对结构动力性能的影响规律,并给出相应实际工程的改善措施。

The transfer matrix method is used to solve the in-plane eigenvalue problem during the cantilever construction of arch bridges,and an evaluation method for solving in-plane vertical bending stiffness during construction of this type of bridge is established.Firstly,the cables and arches are regarded respectively as tensioned strings with no sag and Euler Bernoulli beams,and the total transfer matrix of the system is derived based on the basic theory of the transfer matrix method,and then the frequencies and modes of the system are calculated by considering the eigenvalue equation of the system combining the boundary conditions of the arch and the cables and the displacement of the cable-arch nodes.Meanwhile,the finite element analysis software ANSYS 15.0 was used to establish the finite element model of an arch bridge in the closed state and obtain the frequencies and modes solution.The comparison of results of the proposed method in this paper and the finite element method shows the correctness of the present method and model in this paper.Then,the above-mentioned theoretical method and finite element method are applied to analyze and compare the frequencies and modes of the half-span model before the arch bridge is closed.The consistent results of the two method further illustrate the correctness of the method and model in this paper.Finally,the modulus of elasticity and the initial force of the cables,the radius of the arch bridge and other parameters are selected as factors that affect the natural frequencies of the structure.A systematic parametric analysis of the first six-order frequencies of the model is carried out,and the influence principle of the design parameters of the arch bridge and of the cables in the closed state on the dynamic performance of the structure is obtained,and the corresponding improvement measures for the actual project are given.