箱梁的空间振动分析探讨

本文采用三角形板单元对箱梁分段建立运动微分方程,解出模态,对整体结构动态综合时进行了缩阶,求出结构的低频模态。在Zienkiewicz处理单元刚度矩阵奇异问题方法的基础上,提出采用假设板单元面内转动质量系数的方法处理质量矩阵的奇异问题。本文还用坐标总集推导了总装方程,结果表明,所作近似与各分段模态间之正交性等价。算例表明:对板单元刚度、质量矩阵奇异性问题在不计结点之面内转动自由度时之处理方法将是可行的。有限元法与动态子结构法结合(简称FEDS)对箱梁进行动态分析是有效的。

A Spacial Vibration Analysis of Box Girders

In this paper, the differential equations of motion for box girder segments are established and solved using the triangular-plate elements. A kind of constrained modal synthesis method with truncated modal matrices is then used to construct the global differential equations of motion, obtaining the girder modes of lower frequencies. Based on the method of treating a kind of singularity in stiffness matrix by Zienkiewicz, the paper suggests to introduce a set of empirical in-plane rotational inertia in the inertia matrix. Another approach for the synthesis equations is executed to show the orthogonality existing for the approximation introduced in the synthesis. Calculation of some examples shows that the treatment in cases with certain singularity problem of stiffness and inertia matrices is feasible, and the combination of finite element method and dynamic substructure method is effective in dynamic analysis of the box girders.