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城市交通系统中宽扁梁结构的自由振动分析
引用本文:蒋吉清,李钢,魏纲,魏新江,孙泽星.城市交通系统中宽扁梁结构的自由振动分析[J].城市轨道交通研究,2017,20(8).
作者姓名:蒋吉清  李钢  魏纲  魏新江  孙泽星
作者单位:1. 浙江大学城市学院工程分院,310015,杭州;2. 铁道第三勘察设计院集团有限公司,300450,天津
基金项目:浙江省自然科学基金项目,国家自然科学基金项目
摘    要:为研究城市交通系统中宽扁梁的动力性能,由明德林(Mindlin)板理论退化得到板梁的控制方程,并推导出两端简支和两端固支板梁的自由振动特征方程,然后分别求解其自振频率和模态,并将计算结果与铁木辛科(Timoshenko)梁、Mindlin板的结果进行对比,总结板梁方程的梁宽适用范围并考虑泊松比对宽梁自由振动的影响。分析表明:相较Timoshenko梁方程,板梁方程更贴近Mindlin板的计算结果,尤其是前5阶自振频率,更适于较大泊松比的宽梁结构动力分析。

关 键 词:明德林板理论  板梁  铁木辛科梁  自振频率  振动模态

Analysis of Plate-beam Free Vibration in Urban Traffic System
JIANG Jiqing,LI Gang,WEI Gang,WEI Xinjiang,SUN Zexing.Analysis of Plate-beam Free Vibration in Urban Traffic System[J].Urban Mass Transit,2017,20(8).
Authors:JIANG Jiqing  LI Gang  WEI Gang  WEI Xinjiang  SUN Zexing
Abstract:To study the dynamic analysis of plate-beam,the governing equations are derived from the Mindlin plate theo-ry,the characteristic equations of simply-supported ends and clamped-clamped beam ends are obtained respectively. Then, the natural frequency and normal mode are calculated and compared with those of the Timoshenko beam and Mindlin plate,a suitable range of length-to-width ratio is concluded for the application of the plate-beam theory and the influence of Poisson's ratio on the free vibration of wide beam. As the result,the plate-beam theory is proved to have better agree-ment with the Mindlin plate theory rather than the Timoshenko beam equations,especially for the first five frequencies.
Keywords:Mindlin plate theory  plate-beam  Timoshenko beam  natural frequency  vibration mode
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