薄壁箱梁剪滞剪切效应自振特性分析

Natural Vibration Frequency Analysis of Thin-wall Box Beam Considering Both Shear Lag and Shear Deformation

在推导考虑剪力滞、剪切变形双重效应的单元刚度矩阵与等效结点荷载矩阵的基础上[1],进一步推导出考虑双重效应的单元质量矩阵,从而形成完整的薄壁箱梁考虑双重效应的矩阵分析体系,可方便地纳入矩阵位移法程序系统,为常见的薄壁连续梁等复杂结构的剪力滞效应分析提供一种计算手段。利用自编程序ZLBOX对薄壁箱型简支梁和悬臂梁考虑剪力滞、剪切变形双重效应时的自振特性进行了分析,所得结果与ANSYS实体单元计算结果符合良好。计算结果表明,剪力滞、剪切变形双重效应使薄壁箱梁的自振频率降低,剪力滞效应占双重效应的85%以上,双重效应对高阶频率的影响比低阶频率的影响大。

Based on the minimum potential energy principle,the differential equations considering both the shear lag and shear deformation were established, and the finite element stiffness matrix and mass matrix were derived. The whole matrix analyzed system considering both the shear lag and shear deformation has been established successfully, the calculation method can be brought into the matrix displacement system conveniently, and it is a new calculation method to deal with the complex thin wall continuous girder structure. The natural vibration frequencies of the simply supported box beam and cantilever box beam considering both the shear lag and shear deformation are analyzed by using the ZLBOX program, the numerical calculation results accord with those from the ANSYS. This shows the natural vibration frequencies of the thin-wall box beams will decrease because of the concurrence of both the shear lag and shear deformation. The proportion of shear lag contributing to the natural vibration frequency falling is over 85%, and the dual influence of both the shear lag and shear deformation on high frequencies is larger than that on low frequencies.