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移动荷载作用下具有不确定参数桥梁动力响应分析

刘凡 李利祥 赵岩

刘凡,李利祥,赵岩. 移动荷载作用下具有不确定参数桥梁动力响应分析 [J]. 应用数学和力学,2023,44(3):241-247 doi: 10.21656/1000-0887.430148
引用本文: 刘凡,李利祥,赵岩. 移动荷载作用下具有不确定参数桥梁动力响应分析 [J]. 应用数学和力学,2023,44(3):241-247 doi: 10.21656/1000-0887.430148
LIU Fan, LI Lixiang, ZHAO Yan. Dynamic Responses Analysis of Bridges With Uncertain Parameters Under  Moving Loads[J]. Applied Mathematics and Mechanics, 2023, 44(3): 241-247. doi: 10.21656/1000-0887.430148
Citation: LIU Fan, LI Lixiang, ZHAO Yan. Dynamic Responses Analysis of Bridges With Uncertain Parameters Under  Moving Loads[J]. Applied Mathematics and Mechanics, 2023, 44(3): 241-247. doi: 10.21656/1000-0887.430148

移动荷载作用下具有不确定参数桥梁动力响应分析

doi: 10.21656/1000-0887.430148
基金项目: 国家自然科学基金(11772084;U1906233);国家重点研发计划(2017YFC0307203);山东省重点研发计划(2019JZZY010801)
详细信息
    作者简介:

    刘凡(1992—),男,博士生(E-mail:dlut_liufan@mail.dlut.edu.cn

    赵岩(1974—),男,教授,博士,博士生导师(通讯作者. E-mail:yzhao@dlut.edu.cn

  • 中图分类号: O321

Dynamic Responses Analysis of Bridges With Uncertain Parameters Under  Moving Loads

  • 摘要:

    针对具有不确定参数桥梁在移动荷载作用下的动力响应分析,首次建立了移动荷载作用下桥梁响应分析的多项式维数分解法。将结构的不确定参数视为独立的随机变量,构造了结构动力响应关于不确定参数的随机函数;进而采用一组变量数目逐次增加的成员函数实现结构动力响应的维数分解,并利用Fourier多项式展开推导成员函数的近似显式表达。通过降维积分方法降低概率空间内的积分维度,高效地实现了展开系数的计算。在数值算例中,进行了具有不确定参数桥梁在移动荷载作用下的响应估计,并与Monte-Carlo模拟进行对比,验证了该文方法的精确性和效率。

  • 图  1  受移动集中荷载作用的简支梁桥

    Figure  1.  A simply supported beam bridge subjected to moving loads

    图  2  桥梁跨中位移均值

    Figure  2.  The mean of displacement

    图  3  桥梁跨中位移标准差

    Figure  3.  The SD of displacement

    图  4  $ t=0.8\;\mathrm{s} $时跨中位移的概率密度

    Figure  4.  The probability density of displacement at $ t=0.8\;\mathrm{s} $

    图  5  位移样本曲线

    Figure  5.  Sample curves of displacement

    图  6  大跨度斜拉桥

    Figure  6.  The long-span cable-stayed bridge

    图  7  位移均值

    Figure  7.  The mena of displacement

    图  8  位移标准差

    Figure  8.  The SD of displacement

    图  9  $ t=10.60\;\mathrm{s} $时的概率密度

    Figure  9.  The probability density at $ t=10.60\;\mathrm{s} $

    图  10  概率密度演化曲线

    Figure  10.  Evolution curves of the probability density

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出版历程
  • 收稿日期:  2022-04-27
  • 修回日期:  2022-06-17
  • 网络出版日期:  2023-03-20
  • 刊出日期:  2023-03-15

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