薄壁曲线箱梁空间振动分析方法  

3-D Vibration Analytical Method of Thin-walled Curved Box Girder

作　　者：蔡恒 卢海林 颜燕祥 严若愚 CAI Heng;LU Hailin;YAN Yanxiang;YAN Ruoyu(School of Civil Engineering,Wuhan University,Wuhan 430072,China;School of Civil Engineering and Architecture,Wuhan Institute of Technology,Wuhan 430074,China)

机构地区：[1]武汉大学土木建筑工程学院,湖北武汉430072 [2]武汉工程大学土木工程与建筑学院,湖北武汉430074

出　　处：《铁道学报》2019年第6期124-129,共6页Journal of the China Railway Society

基　　金：国家自然科学基金(51378404)

摘　　要：通过在结点中引入高阶位移插值函数构造形函数矩阵,基于虚功原理和动力有限元理论,推导每个结点11自由度的薄壁曲线箱梁空间单元刚度矩阵和质量矩阵。在推导刚度矩阵时综合考虑薄壁曲线箱梁的拉压、弯曲、扭转、翘曲、畸变和剪力滞效应;在推导质量矩阵时,考虑扭心、畸心与质心不重合的影响。通过MATLAB编制相应的计算程序,求解薄壁曲线箱梁的前5阶自振频率和相应的振型,经与ANSYS板壳单元数值结果比较,吻合良好。本文沿梁长方向划分为数个单元便取得满意效果,所提出的方法可为桥梁结构抗震、抗风和车致振动计算提供依据。The form function matrix was created by introducing high order displacement interpolation function in the node. Based on virtual work principle and dynamic finite element theory, the spatial element stiffness matrix and mass matrix of thin-walled box girder with 11 degrees of freedom in each node were deduced. The effects of tension-compression, bending, torsion, warping, distortion and shear lag were comprehensively considered in deducing stiffness matrix. The effects of non-coincidence of mass center with torsion center and distortion center were also considered in deducing mass matrix. The first 5 natural vibration frequencies and corresponding modes of thin-walled curved box girder were solved on MATLAB. A comparison of the results of present work with numerical results of ANSYS shell element shows that they agree well with each other. Satisfactory results can be obtained by dividing the beam into several elements along longitudinal direction. The proposed method can provide a basis for the calculation of seismic, wind and vehicle-induced vibration of bridge structures.

关 键 词：薄壁曲线箱梁 振动频率 刚度矩阵 质量矩阵 有限元 

分 类 号：U448.42[建筑科学—桥梁与隧道工程] U448.213[交通运输工程—道路与铁道工程]