变截面连续梁动力特性的差分解法  

Finite-difference methods for calculating dynamic properties of variational continuous beams

作　　者：吴辉琴[1] 王赞芝[1] 涂辉[1] 赵华营[1] 

机构地区：[1]广西工学院土木建筑工程系,广西柳州545006

出　　处：《广西大学学报（自然科学版）》2010年第1期101-104,共4页Journal of Guangxi University（Natural Science Edition）

基　　金：广西自然科学基金资助项目(桂科自:0481002);广西工学院博士基金科研项目

摘　　要：针对变截面连续梁在公路、铁路桥梁、建筑、机械结构中广泛使用的情况,为解决变截面连续梁的变系数控制微分方程无法得到解析解这一困难,提出了运用有限差分方法解此问题的方法。通过推导连续梁动力特性的振型方程,建立其差分格式,利用对称性、反对称性、边界条件,将差分方程组简化,求解振型系数行列式为0这一方程,得到自振频率,相应地求出振型,并应用到实际跨线桥的计算。结果表明,差分方解法解决连续梁的振动问题非常有效,应用步骤简洁、固定。按照此思路编制计算机专用程序能对任意多跨变截面梁进行动力分析,可适用于土木、机械、舰船等结构。In highway and railway engineering, continuous bridges are usually made up with variable section along the span in order to reduce its designed positive bending moment in the mid-span, and also to provide convenience of arranging the prestressed bars on the top of the cross section. In the paper, the vibrating mode equations were deduced at first, and then, the difference schemes of the equations were established. By utilizing the symmetry, antisymmetry, and boundary conditions, the difference equations were simplified. Based on the fact that it is impossible for all the deflections being zero in each node, taking the coefficient determinant to be zero, an equation with the square of natural frequencies as unknown was generated. By solving the equation, the natural frequencies were obtained in the end.

关 键 词：变截面 连续梁 差分解法 

分 类 号：U442.55[建筑科学—桥梁与隧道工程]