为了提高薄壁箱梁自由振动的高阶固有频率解的精确度，提出了一种通用的数学方法，分析薄壁箱梁的自由振动特性，包含了其横截面形变的影响。基于广义坐标原理，利用虚功变分原理推导出运动控制方程，在相应的边界条件和连续条件下，运用微分变换法求解分析固有频率。该模型考虑了箱梁截面的翘曲和畸变形变，具有一定的通用性和有效性。算例分析中，计算薄壁箱梁的固有频率和绘制模态振型图，并与已知文献进行比较可知:本文求解固有频率的理论方法与已知文献的结果有较好的吻合度，此方法通过考虑畸变效应影响提高薄壁箱梁的自由振动固有频率的精确度，且可通用于不同边界条件下的箱梁固有频率计算；在振型分析中，横向位移和畸变形变占有重要地位。
关键词：弯曲；翘曲；扭转；畸变；微分变换法
Abstract
In order to improve the accuracy of the higher order natural frequency solution of the free vibration of thin-walled box girder, a general mathematical method is proposed to analyze the free vibration characteristics of thin-walled box girder, including the influence of cross-section deformation. Based on the generalized coordinate principle, the governing equations of motion and the corresponding boundary conditions and continuous conditions are derived by the variational principle of virtual work, and then solved by the differential transformation method. The model takes into account the warping and distortion deformation of the box girder loading surface, which has universality and effectiveness. In the example analysis, the natural frequencies were calculated and the mode shape diagrams were drawn. Compared with the known literature, it can be seen that: The theoretical method of solving natural frequency in this paper is in good agreement with the results of known literatures. This methods improves the accuracy of natural frequency of free vibration of thin-walled box girder by considering distortion effect. It can be used to calculate the natural frequency of box girder under different boundary conditions. Transverse deformation and distortion deformation play an important role in the mode diagrams.
Key words: bending; warping; torsion; distortion; Differential transform method
关键词
弯曲 /
翘曲 /
扭转 /
畸变 /
微分变换法
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Key words
bending /
warping /
torsion /
distortion /
Differential transform method
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参考文献
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