考虑剪切变形影响的斜梁桥自振频率的解析方法  

THEORETICAL METHOD FOR DETERMINING THE VIBRATING FREQUENCY OF SKEWED GIRDER BRIDGES INCLUDING SHEAR DEFORMATION EFFECT

作　　者：杨美良[1] 钟放平 张建仁[1] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004 [2]湖南省长湘高速公路建设开发有限公司,湖南长沙410429

出　　处：《工程力学》2013年第2期104-111,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(50778024);交通运输部长湘高速公路两型科技示范工程项目(CXKJSF0108-3)

摘　　要：斜梁桥振动频率没有显式解,给使用《公路桥涵设计通用规范》方法计算冲击系数带来不便。考虑斜梁桥振动时的弯扭耦合效应,分别采用修正的Timoshenko梁理论建立其弯曲振动的动态刚度矩阵,采用Saint-Venant扭转理论建立其自由扭转振动的动态刚度矩阵,结合斜支承边界条件,导出斜支承坐标系下的动态刚度矩阵,提取弯矩-转角的刚度方程,根据其奇异条件建立关于斜梁桥自振频率的超越方程,采用二分法对超越方程进行求解以得到自振频率。该文分析了一座标准A型单跨斜箱梁桥考虑与不考虑剪切变形影响时的前5阶振动频率随斜交角的变化,比较了正交简支初等梁和正交简支深梁、斜支初等梁和斜支深梁的前5阶频率。结果显示:斜梁桥基频随斜交角的增大而增大、第2阶频率随斜交角的增大而减小;斜梁桥振动频率的计算应采用考虑剪切变形影响的深梁理论。There were no explicit solutions to the vibrating frequencies of skewed girder bridges, and it was difficult to calculate the impact factors by using the empirical method recommended by Chinese general code for the design of highway bridges and culverts. Considering the coupling effect of flexure-torsion vibrating for skewed girder bridges, the modified Timoshenko beam theory was adopted to establish the dynamic flexural stiffness matrix, and Saint-Venant free torsion theory to establish the dynamic torsion stiffness matrix. Incorporating the skewed supporting boundary conditions, the dynamic stiffness matrix of a skewed beam element was derived based on the skewed coordinate. Using the moment-slope finite element stiffness matrix and its singularity, the transcendental equation to determine the free vibration frequency for skewed girder bridges was presented. Using the bisection method, the vibrating frequencies of A-type skewed girder bridges were analyzed. The changing tendencies of the first five orders frequencies for different skew angles were obtained, and the first five orders frequencies of a simply-supported Bernoulli-Euler beam, a simply-supported Timoshenko beam, a skewed-supported Bernoulli-Euler beam and a skewed-supported Timoshenko beam were compared. Some conclusions are summarized that the fundamental frequency augments and the second order frequency decreases with the skewed angles enlarged, Timoshenko beam theory should be adopted in calculating the vibrating frequencies of skewed bridges to include the shear deformation effect.

关 键 词：斜梁桥 弯扭耦合 振动频率 修正Timoshenko梁理论 动态刚度矩阵 超越方程 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]