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考虑畸变的起重机薄壁箱梁的自由振动分析

谭敏尧 程文明 李杭飞 臧付连

谭敏尧, 程文明, 李杭飞, 臧付连. 考虑畸变的起重机薄壁箱梁的自由振动分析[J]. 西南交通大学学报, 2022, 57(5): 1040-1046. doi: 10.3969/j.issn.0258-2724.20200613
引用本文: 谭敏尧, 程文明, 李杭飞, 臧付连. 考虑畸变的起重机薄壁箱梁的自由振动分析[J]. 西南交通大学学报, 2022, 57(5): 1040-1046. doi: 10.3969/j.issn.0258-2724.20200613
TAN Minyao, CHENG Wenming, LI Hangfei, ZANG Fulian. Free Vibration Analysis of Thin-Walled Box Beam of Crane Considering Distortion[J]. Journal of Southwest Jiaotong University, 2022, 57(5): 1040-1046. doi: 10.3969/j.issn.0258-2724.20200613
Citation: TAN Minyao, CHENG Wenming, LI Hangfei, ZANG Fulian. Free Vibration Analysis of Thin-Walled Box Beam of Crane Considering Distortion[J]. Journal of Southwest Jiaotong University, 2022, 57(5): 1040-1046. doi: 10.3969/j.issn.0258-2724.20200613

考虑畸变的起重机薄壁箱梁的自由振动分析

doi: 10.3969/j.issn.0258-2724.20200613
基金项目: 国家自然科学基金(51675450)
详细信息
    作者简介:

    谭敏尧(1987—),女,博士研究生,研究方向为起重机箱形梁结构,E-mail:minyaotan@163.com

    通讯作者:

    程文明(1963—),男,教授,博士,研究方向为起重机及工业工程,E-mail:wmcheng@home.swjtu.edu.cn

  • 中图分类号: U448.213

Free Vibration Analysis of Thin-Walled Box Beam of Crane Considering Distortion

  • 摘要:

    为了提高薄壁箱梁固有频率的计算精确度,基于广义坐标原理,对薄壁箱梁的动力特性进行了分析. 首先,通过虚功原理且考虑畸变形变的影响,获取了5种高度耦合模态(延伸、弯曲、扭转、翘曲和畸变)的自由振动微分方程组;其次,考虑转动惯性运动项的影响,建立了简支边界条件下的运动学模型,获得了薄壁箱形梁自由振动固有频率的四阶代数方程,进而求得固有频率的精确解;最后,通过算例将考虑畸变的固有频率精确解与Prokić 理论以及有限元分析方法的结果进行比较,验证了该方法的有效性和准确性. 结果表明:考虑畸变效应能够更准确地反映高阶状态下薄壁箱形梁的自由振动固有频率;对自由振动的4阶固有频率进行比较,当箱形梁长度为3 m时,本文理论的相对误差相较于Prokić 理论的0.42%下降至0.38%;当箱梁长度分别为4 m和5 m时,相对误差进一步下降至0.30% 和0.40%.

     

  • 图 1  薄壁箱形梁坐标系

    Figure 1.  Coordinate systems of thin-walled box beams

    图 2  薄壁箱形梁的微单元

    Figure 2.  A micro-element of a thin-walled box beam

    图 3  薄壁箱形梁的几何参数

    Figure 3.  Geometrical parameters of thin-walled box beams

    图 4  弯曲模态振型

    Figure 4.  Bending mode shapes

    表  1  薄壁箱形梁其中4阶的固有频率比较

    Table  1.   Comparison of 2-, 4-, 6-, and 8-order natural frequencies of thin-walled box beams

    阶数 ω1/Hz ωFEA/Hz Δ/%
    2 9.36 9.34 0.18
    4 36.99 36.90 0.25
    6 54.30 54.11 0.36
    8 89.46 88.67 0.89
    下载: 导出CSV

    表  2  简支薄壁箱形梁的固有频率

    Table  2.   Natural frequencies of simply supported thin-walled box beams

    L/m 阶数 ω1/Hz ω2/Hz ωFEA/Hz Δ1/% Δ2/%
    3 1 11.92 11.91 11.91 0.06 0
    2 63.16 63.12 63.03 0.20 0.14
    3 64.90 64.08 64.67 0.35 0.20
    4 114.41 114.36 113.93 0.42 0.38
    4 1 7.33 7.33 7.33 0 0
    2 36.87 36.86 36.83 0.10 0.08
    3 50.04 50.01 49.91 0.26 0.20
    4 76.63 76.57 76.34 0.38 0.30
    5 1 5.11 5.11 5.11 0 0
    2 25.79 25.79 25.77 0.08 0.06
    3 35.72 35.71 35.64 0.23 0.19
    4 61.68 61.64 61.47 0.34 0.28
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-09-09
  • 修回日期:  2020-10-30
  • 网络出版日期:  2022-08-09
  • 刊出日期:  2020-11-04

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