曲线梁桥振型主方向判定方法研究

A Method to Determine Main Direction of a Curved Bridge's Mode Shape

由于曲线梁桥独特的构造特点,其振型存在"弯扭耦合"现象。为了判定曲线梁桥各阶"弯扭耦合"振型的主方向是弯曲或纯扭转,把曲线梁桥的每阶振型分解为竖向弯曲、纯扭转、横向弯曲和纵向移动4个子方向,把每阶振型的能量亦分成竖向弯曲能量、扭转能量、横向弯曲能量和沿纵向平移能量4个方向上的能量,引入4个方向参数来分别表示各子方向能量所占各阶振型能量的比值。然后从结构动力学理论知识出发,根据无阻尼系统每阶振型动能和变形能之和为常数的基本原理,推导了4个方向参数的计算公式,推导结果显示,方向系数仅为结构质量、截面几何特性和振型向量的表达式。最后提出了一种根据方向参数值的大小判定曲线梁桥各阶振型以哪个子方向为主的方法,并通过实例介绍了该方法的应用。

Due to the special construction feature, the mode shape of a curved bridge has ＂flexure-torsion coupling＂ situation. In order to determine whether the main direction of the mode shape is flexure or torsion, each mode shape was divided into four sub directions which are vertical bending, pure torsion, transverse bending and longitudinal shift respectively. Accordingly, the energy of each mode was also subdivided into four directions. The ratios between the energy of sub direction and the total energy of a mode were denoted by four direction parameters. Theoretical derivation for the direction parameters was given based on the energy conservation principle of each mode of undamped system. The derivation result reveals that four formulas of the direction parameters are only related to structural mass, sectional geometric characteristics and mode vectors. Finally, the method of determining the main sub direction of mode shapes of a curved bridge was given according to the values of the four parameters, and how to use the method was presented too by a instance.