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磁浮车辆-桥梁耦合系统随机振动分析的时域显式方法研究

陆周瑞 陈冉 苏成

陆周瑞, 陈冉, 苏成. 磁浮车辆-桥梁耦合系统随机振动分析的时域显式方法研究[J]. 工程力学, 2022, 39(8): 19-30. doi: 10.6052/j.issn.1000-4750.2021.04.0321
引用本文: 陆周瑞, 陈冉, 苏成. 磁浮车辆-桥梁耦合系统随机振动分析的时域显式方法研究[J]. 工程力学, 2022, 39(8): 19-30. doi: 10.6052/j.issn.1000-4750.2021.04.0321
LU Zhou-rui, CHEN Ran, SU Cheng. RANDOM VIBRATION ANALYSIS OF MAGLEV VEHICLE-BRIDGE COUPLED SYSTEMS WITH THE EXPLICIT TIME-DOMAIN METHOD[J]. Engineering Mechanics, 2022, 39(8): 19-30. doi: 10.6052/j.issn.1000-4750.2021.04.0321
Citation: LU Zhou-rui, CHEN Ran, SU Cheng. RANDOM VIBRATION ANALYSIS OF MAGLEV VEHICLE-BRIDGE COUPLED SYSTEMS WITH THE EXPLICIT TIME-DOMAIN METHOD[J]. Engineering Mechanics, 2022, 39(8): 19-30. doi: 10.6052/j.issn.1000-4750.2021.04.0321

磁浮车辆-桥梁耦合系统随机振动分析的时域显式方法研究

doi: 10.6052/j.issn.1000-4750.2021.04.0321
基金项目: 国家自然科学基金项目(51678252);广东省现代土木工程技术重点实验室项目(2021B1212040003)
详细信息
    作者简介:

    陆周瑞(1996−),男,重庆人,硕士生,主要从事车桥耦合随机振动问题研究(E-mail: 1075214731@qq.com)

    陈 冉(1988−),男,广东人,助理研究员,博士,主要从事车桥耦合随机振动和结构健康监测研究(E-mail: ranchen@scut.edu.cn)

    通讯作者:

    苏 成(1968−),男,广东人,教授,博士,博导,主要从事结构随机振动和计算力学研究(E-mail: cvchsu@scut.edu.cn)

  • 中图分类号: O324;U237

RANDOM VIBRATION ANALYSIS OF MAGLEV VEHICLE-BRIDGE COUPLED SYSTEMS WITH THE EXPLICIT TIME-DOMAIN METHOD

  • 摘要: 轨道不平顺所引起的磁浮车辆-桥梁耦合系统随机振动问题是磁浮列车行驶过程中需要关注的重点问题之一,传统的随机振动方法在解决这类问题时存在工作量大、计算效率低等问题。分别从磁浮车辆系统和桥梁系统出发,建立磁浮车辆系统响应和桥梁系统响应关于车桥相互作用电磁力的时域显式表达式;利用车轨间的电磁力方程及几何相容条件,构建电磁力关于轨道不平顺的时域显式表达式;进一步推导得到轨道不平顺作用下磁浮车辆系统和桥梁系统关键动力响应显式表达式。在此基础上,利用统计矩运算法则,直接获得磁浮车辆系统和桥梁系统关键响应的演变统计矩;也可以利用轨道不平顺的数字生成技术,结合随机模拟法,获得车桥耦合系统关键响应的统计信息。在上述过程中,由于车桥耦合系统关键动力响应的显式表达式已先行构建完毕,因此大幅提升了随机振动分析的计算效率。以二自由度磁浮车辆与桥梁耦合模型为例,阐明了方法列式过程。磁浮列车过多跨简支梁桥的数值算例结果表明,时域显式法具有理想的计算精度和效率。
  • 图  1  二自由度磁浮车辆-桥梁耦合系统力学模型

    Figure  1.  Mechanical model for a 2-DOF maglev vehicle-bridge coupled system

    图  2  某轨道不平顺样本

    Figure  2.  A sample of guideway irregularity

    图  3  桥梁跨中竖向位移${y_{{\text{bm}}}}$时程

    Figure  3.  Time history of vertical displacement ${y_{{\text{bm}}}}$ at mid-span of bridge

    图  4  车体竖向加速度${a_1}$时程

    Figure  4.  Time history of vertical acceleration ${a_1}$ of car body

    图  5  电流变化量$\Delta I$时程

    Figure  5.  Time history of electric current change $\Delta I$

    图  6  悬浮间隙变化量$\Delta c$时程

    Figure  6.  Time history of air gap change $\Delta c$

    图  7  桥梁跨中竖向位移${y_{{\text{bm}}}}$均值时程

    Figure  7.  Time history of mean value of vertical displacement ${y_{{\text{bm}}}}$ at mid-span of bridge

    图  8  桥梁跨中竖向位移${y_{{\text{bm}}}}$标准差时程

    Figure  8.  Time history of standard deviation of vertical displacement ${y_{{\text{bm}}}}$ at mid-span of bridge

    图  9  车体竖向加速度${a_1}$均值时程

    Figure  9.  Time history of mean value of vertical acceleration ${a_1}$ of car body

    图  10  车体竖向加速度${a_1}$标准差时程

    Figure  10.  Time history of standard deviation of vertical acceleration ${a_1}$ of car body

    图  11  电流变化量$\Delta I$均值时程

    Figure  11.  Time history of mean value of electric current change $\Delta I$

    图  12  电流变化量$\Delta I$标准差时程

    Figure  12.  Time history of standard deviation of electric current change $\Delta I$

    图  13  悬浮间隙变化量$\Delta c$均值时程

    Figure  13.  Time history of mean value of air gap change $\Delta c$

    图  14  悬浮间隙变化量$\Delta c$标准差时程

    Figure  14.  Time history of standard deviation of air gap change $\Delta c$

    图  15  磁浮列车过多跨简支梁桥模型

    Figure  15.  Mechanical model for a maglev train traversing a multi-span simply-supported bridge

    图  16  某跨简支梁跨中竖向位移${y_{{\text{bm}}}}$均值时程

    Figure  16.  Time history of mean value of vertical displacement ${y_{{\text{bm}}}}$ at mid-span of a simply-supported beam

    图  17  某跨简支梁跨中竖向位移${y_{{\text{bm}}}}$标准差时程

    Figure  17.  Time history of standard deviation of vertical displacement ${y_{{\text{bm}}}}$ at mid-span of a simply-supported beam

    图  18  第2节车辆车体竖向加速度${a_1}$均值时程

    Figure  18.  Time history of mean value of vertical acceleration ${a_1}$ for car body of the 2nd maglev vehicle

    图  19  第2节车辆车体竖向加速度${a_1}$标准差时程

    Figure  19.  Time history of standard deviation of vertical acceleration ${a_1}$ for car body of the 2nd maglev vehicle

    表  1  单样本时程分析耗时对比

    Table  1.   Comparison of computation time for sample analysis

    方法计算耗时/s
    时域显式法0.739 + 0.013 = 0.752
    Newmark-β逐步迭代法1.413
    下载: 导出CSV

    表  2  算例1响应统计矩分析的计算耗时

    Table  2.   Computation time for statistical moment analysis of responses for the 1st numerical example

    方法样本数计算耗时/s
    显式表达式建立响应统计矩分析总耗时
    时域显式直接法0.7390.1000.839
    时域显式随机模拟法2000.0720.811
    6000.1620.901
    10000.2110.950
    30000.5021.241
    50000.6931.432
    下载: 导出CSV

    表  3  各响应平均峰值

    Table  3.   Mean peak values of responses

    样本数响应平均峰值
    ${y_{{\text{bm,peak}}}}{\text{/m}}$${a_{ {{1} },{\text{peak} } } }/({\text{m/} }{ {\text{s} }^2})$$\Delta {I_{{\text{peak}}}}/{\text{A}}$$\Delta {c_{{\text{peak}}}}/{\text{m}}$
    2001.157×10−20.4092.8416.677×10−4
    6001.157×10−20.4112.8656.740×10−4
    10001.157×10−20.4112.8696.751×10−4
    30001.157×10−20.4142.8806.770×10−4
    50001.157×10−20.4152.8836.781×10−4
    下载: 导出CSV

    表  4  算例2响应统计矩分析的计算耗时

    Table  4.   Computation time for statistical moment analysis of responses for the 2nd numerical example

    方法计算耗时/s
    显式表达式
    建立
    响应统计矩
    分析
    总耗时
    时域显式
    直接法
    5.89411.85017.744
    时域显式
    随机模拟法
    4.582
    (1000个样本)
    10.476
    下载: 导出CSV
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  • 收稿日期:  2021-04-28
  • 修回日期:  2021-08-06
  • 网络出版日期:  2021-08-27
  • 刊出日期:  2022-08-25

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