改进型波形钢腹板组合箱梁的动力特性分析

Dynamic Behavior Analysis of Improved Composite Box Girder with Corrugated Steel Webs

研究目的:为了给考虑剪滞剪切效应波形钢腹板-钢底板-混凝土顶板(简称改进型波形钢腹板,即CSWSB)组合箱梁动力特性计算提供一种新的计算方法,本文通过考虑剪滞剪切变形效应和顶底板的不同材料属性,推导出CSWSB组合箱梁的控制微分方程组及其解析解,以及该类型组合箱梁的单元刚度矩阵、等效结点荷载列阵、一致质量矩阵,并以杆系结构有限单元法为基础编制求解广义特征值的Matlab程序,且采用等效刚度法对传统波形钢腹板(简称CSW)和CSWSB组合箱梁的动力特性进行对比。研究结论:(1)CSWSB组合箱梁在考虑了剪滞剪切变形效应后的振动频率均有不同程度的减小,且随着振动频率阶数的增加,影响程度也逐渐变大,在四阶时达到了40%;(2)按照刚度等效原则换算得到CSW组合箱梁的自振频率均小于CSWSB组合箱梁的自振频率,振型模态完全吻合,振动趋势一致;(3)对CSWSB组合箱梁进行动力特性分析时应考虑剪力滞和剪切变形效应的影响,且采用换算截面法对CSWSB组合箱梁进行动力分析是可靠的。

Research purposes:To provide a new method for calculating the dynamic characteristics of corrugated steel webs-steel bottom-concrete roof(CSWSB)composite box girder considering shear lag shear effect,considering shear lag shear deformation effect and different material properties of roof and floor,the governing differential equations and their analytical solutions of CSWSB composite box girders are derived.The element stiffness matrix,equivalent nodal load matrix and uniform mass matrix of this type of composite box girders are also derived.Based on the finite element method of bar structure,the generalized characteristics for solving the problems are worked out.The dynamic characteristics of traditional corrugated steel webs(CSW)and CSWSB composite box girders are compared by means of equivalent stiffness method with the eigenvalue of MATLAB program.Research conclusions:(1)The vibration frequency of CSWSB composite box girders decreases in varying degrees after considering the shear lag shear deformation effect,and with the increase of the vibration frequency order,the influence degree increases gradually,reaching 40%at the fourth order.(2)According to the principle of equivalent stiffness,the natural frequencies of CSW composite box girders are less than those of CSWSB composite box girders,and the mode shapes are identical,and the vibration trends are identical.(3)The effect of shear lag and shear deformation should be considered in the dynamic analysis of CSWSB composite box girder,and the dynamic analysis of CSWSB composite box girder by converted section method is reliable.