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含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析

王永亮 王建辉 张磊

王永亮, 王建辉, 张磊. 含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析[J]. 工程力学, 2021, 38(10): 24-33. doi: 10.6052/j.issn.1000-4750.2020.10.0708
引用本文: 王永亮, 王建辉, 张磊. 含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析[J]. 工程力学, 2021, 38(10): 24-33. doi: 10.6052/j.issn.1000-4750.2020.10.0708
WANG Yong-liang, WANG Jian-hui, ZHANG Lei. ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR FREE VIBRATION DISTURBANCE OF CIRCULARLY CURVED BEAMS WITH MULTIPLE CRACKS[J]. Engineering Mechanics, 2021, 38(10): 24-33. doi: 10.6052/j.issn.1000-4750.2020.10.0708
Citation: WANG Yong-liang, WANG Jian-hui, ZHANG Lei. ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR FREE VIBRATION DISTURBANCE OF CIRCULARLY CURVED BEAMS WITH MULTIPLE CRACKS[J]. Engineering Mechanics, 2021, 38(10): 24-33. doi: 10.6052/j.issn.1000-4750.2020.10.0708

含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析

doi: 10.6052/j.issn.1000-4750.2020.10.0708
基金项目: 国家自然科学基金项目(41877275,51608301);中央高校基本科研业务费专项资金项目(2019QL02);天津市重点实验室开放课题基金项目(2017SCEEKL003);中国矿业大学(北京)越崎青年学者计划项目(2019QN14);大学生创新创业训练计划项目(C201906327,C202006976)
详细信息
    作者简介:

    王建辉(1997−),男,河北石家庄人,硕士生,主要从事矿山岩体计算力学的研究(E-mail: wangjianhui@students.cumtb.edu.cn)

    张 磊(1998−),男,河北廊坊人,本科生,主要从事矿山岩体计算力学的研究(E-mail: zhanglei@students.cumtb.edu.cn)

    通讯作者:

    王永亮(1985−),男,河北唐山人,副教授,博士,硕导,主要从事矿山岩体计算力学的研究(E-mail: wangyl@cumtb.edu.cn)

  • 中图分类号: O242.21

ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR FREE VIBRATION DISTURBANCE OF CIRCULARLY CURVED BEAMS WITH MULTIPLE CRACKS

  • 摘要: 该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实施微裂纹损伤诱发截面弱化,实现多裂纹深度、位置、数目的模拟。引入变截面Timoshenko梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁自由振动问题,得到优化的网格和满足预设误差限的高精度自振频率和振型解答,研究多裂纹损伤对圆弧曲梁振型的扰动行为。数值算例表明,该算法中网格非均匀加密可适应裂纹损伤引起的振型变化,应用于各类曲梁夹角和裂纹损伤分布工况下的自由振动研究,定量分析了多裂纹损伤深度、数目、分布对圆弧曲梁自振频率和振型的扰动影响,检验了该文算法的精确性和实用性。
  • 图  1  含裂纹损伤曲梁坐标系和符号

    Figure  1.  Coordinate systems and symbols of cracked curved beam

    图  2  无裂纹损伤1/4圆弧曲梁模型

    Figure  2.  Model of a quarter of uncracked circularly curved beam

    图  3  裂纹损伤1/4圆弧曲梁振型

    Figure  3.  Vibration modes of a quarter of uncracked circularly curved beam

    图  4  单裂纹损伤曲梁不同裂纹深度(α=0.0、0.16、0.5,β=0. 6125)模型

    Figure  4.  Model of curved beam with single crack in different depth cases (α=0.0, 0.16, 0.5, β =0.6125)

    图  5  裂纹深度对自振频率扰动影响

    Figure  5.  Disturbance influence of crack depth on natural frequencies

    图  6  单裂纹损伤曲梁裂纹深度α=0.5下振型

    Figure  6.  Vibration modes of curved beam with single crack in depth case α=0.5

    图  7  单裂纹损伤曲梁裂纹深度α=0.16下振型扰动

    Figure  7.  Vibration modes disturbance of curved beam with single crack in depth case α=0.16

    图  8  单裂纹损伤曲梁裂纹深度α=0.5下振型扰动

    Figure  8.  Vibration modes disturbance of curved beam with single crack in depth case α=0.5

    图  9  多裂纹损伤曲梁不同裂纹数目(n=2、3、4)模型

    Figure  9.  Model of curved beam with multiple cracks in different number cases (n=2, 3, 4)

    图  10  裂纹数目对自振频率扰动影响

    Figure  10.  Disturbance influence of crack number on natural frequencies

    图  11  多裂纹损伤曲梁不同裂纹数目振型扰动

    Figure  11.  Vibration modes disturbance of curved beam with multiple cracks in different number cases

    图  12  多裂纹损伤曲梁不同裂纹分布模型

    Figure  12.  Model of curved beam with multiple cracks in different distribution cases

    图  13  裂纹分布对自振频率扰动影响

    Figure  13.  Disturbance influence of crack distribution on natural frequencies

    图  14  多裂纹损伤曲梁不同裂纹分布振型扰动

    Figure  14.  Vibration modes disturbance of curved beam with multiple cracks in different distribution cases

    表  1  无裂纹损伤1/4圆弧曲梁自振频率值

    Table  1.   Natural frequencies of a quarter of uncracked circularly curved beam

    阶次k频率值单元数误差/(×10−6)
    $\omega _k^{\rm{h}}$$\omega _k^{\rm{h}}$[29]
    11.641 294 011.641 294 00200.004
    21.894 921 531.894 920 42200.383
    32.888 817 912.888 817 87280.010
    43.929 098 423.929 098 42320.205
    54.462 234 014.462 234 00320.002
    下载: 导出CSV

    表  2  单裂纹损伤曲梁不同裂纹深度自振频率值

    Table  2.   Natural frequencies of curved beam with single crack in different depth cases

    阶次k频率值(α=0.0)误差/(×10−2)频率值(α=0.16)误差/(×10−2)频率值(α=0.5)误差/(×10−2)
    $\omega _{0.0,k}^{\rm{h}}$$\omega _{0.0,k}^{\rm{h}}$[14]$\omega _{0.0,k}^{\rm{h}}$[6]$\omega _{0.16,k}^{\rm{h}}$$\omega _{0.16,k}^{\rm{h}}$[14]$\omega _{0.16,k}^{\rm{h}}$[6]$\omega _{0.5,k}^{\rm{h}}$$\omega _{0.5,k}^{\rm{h}}$[14]$\omega _{0.5,k}^{\rm{h}}$[6]
    124.4450624.4524.520.0224.4272524.4424.480.0524.2146824.3424.320.49
    261.6978861.7361.780.0561.6778861.7261.720.0761.3552761.6861.600.52
    3119.07079119.19118.050.10118.83333119.16117.760.27116.41556118.27116.431.55
    4188.20437188.51184.110.16188.20171188.49184.030.15188.10660188.09183.810.88
    5277.18047277.87269.020.25276.75348277.85268.240.39272.57374277.25267.941.68
    下载: 导出CSV

    表  3  多裂纹损伤数目和位置工况

    Table  3.   Number and location of multiple cracks damage

    工况裂纹数目n裂纹位置β
    20.3333、0.6667
    30.2500、0.5000、0.7500
    40.2000、0.4000、0.6000、0.8000
    下载: 导出CSV

    表  4  多裂纹损伤曲梁不同裂纹数目自振频率值

    Table  4.   Natural frequencies of curved beam with multiple cracks in different number cases

    阶次k频率值
    $\omega _k^{\rm{h}}$,n=2$\omega _k^{\rm{h}}$,n=3$\omega _k^{\rm{h}}$,n=4
    148.535 332 1347.902 077 5847.343 023 95
    2153.660 750 2146.651 275 1144.728 906 6
    3299.120 913 1310.041 195 0292.354 186 0
    4489.649 892 8482.873 507 0505.824 971 0
    5751.539 627 1719.674 070 5712.041 973 3
    102545.139 009 02515.668 639 02502.870 283 0
    207706.363 308 07603.176 785 07520.409 513 0
    3016 025.943 200 016 158.552 250 016 094.761 810 0
    4026 133.888 910 026 108.549 720 026 050.598 210 0
    5038 202.443 860 037 858.824 340 037 728.935 150 0
    下载: 导出CSV

    表  5  多裂纹损伤曲梁不同裂纹分布自振频率值

    Table  5.   Natural frequencies of curved beam with multiple cracks in different distribution cases

    阶次k频率值
    $\omega _{{\rm{u}}k}^h$多裂纹
    均匀分布
    $\omega _{{\rm{c}}k}^h$多裂纹
    左侧集中分布
    频率差
    $\omega _{{\rm{c}}k}^h - \omega _{{\rm{u}}k}^h$
    146.808 799 6747.106 856 430.298 06
    2143.036 785 3144.704 910 701.668 13
    3288.869 077 2290.343 790 101.474 71
    4471.643 268 9477.601 844 005.958 58
    5751.792 226 0703.902 905 80−47.889 32
    102461.536 651 02513.568 991 0052.032 34
    207578.276 595 07536.887 673 00−41.388 92
    3016 051.321 530 016 049.900 190 00−1.421 34
    4026 044.720 800 025 984.653 450 00−60.067 35
    5037 833.740 600 037 557.169 530 00−276.571 07
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-10-04
  • 修回日期:  2020-12-17
  • 网络出版日期:  2021-02-08
  • 刊出日期:  2021-10-18

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