• ISSN 0258-2724
  • CN 51-1277/U
  • EI Compendex
  • Scopus 收录
  • 全国中文核心期刊
  • 中国科技论文统计源期刊
  • 中国科学引文数据库来源期刊

基于拟不可积哈密顿理论的桥梁动力可靠度计算

赫中营,  王根会,  叶爱君,  夏修身

downloadPDF
文章导航 > 西南交通大学学报  > 2016 >  29(1): 50-56.
赫中营, 王根会, 叶爱君, 夏修身. 基于拟不可积哈密顿理论的桥梁动力可靠度计算[J]. 西南交通大学学报, 2016, 29(1): 50-56. doi: 10.3969/j.issn.0258-2724.2016.01.008
引用本文: 赫中营, 王根会, 叶爱君, 夏修身. 基于拟不可积哈密顿理论的桥梁动力可靠度计算[J]. 西南交通大学学报, 2016, 29(1): 50-56. doi: 10.3969/j.issn.0258-2724.2016.01.008
shu
HE Zhongying, WANG Genhui, YE Aijun, XIA Xiushen. Dynamic Reliability Calculation of Bridge Based on Quasi-non-integrable-Hamiltonian System Theory[J]. Journal of Southwest Jiaotong University, 2016, 29(1): 50-56. doi: 10.3969/j.issn.0258-2724.2016.01.008
Citation: HE Zhongying, WANG Genhui, YE Aijun, XIA Xiushen. Dynamic Reliability Calculation of Bridge Based on Quasi-non-integrable-Hamiltonian System Theory[J]. Journal of Southwest Jiaotong University, 2016, 29(1): 50-56. doi: 10.3969/j.issn.0258-2724.2016.01.008
shu

基于拟不可积哈密顿理论的桥梁动力可靠度计算

doi: 10.3969/j.issn.0258-2724.2016.01.008
基金项目: 

国家973计划资助项目(2013CB036302)

国家自然科学基金资助项目(51368033)

详细信息
    作者简介:

    赫中营(1980-),男,讲师,博士,研究方向为桥梁抗震与振动控制、桥梁健康诊断与维修加固,E-mail:0hezhy89@tongji.edu.cn

Dynamic Reliability Calculation of Bridge Based on Quasi-non-integrable-Hamiltonian System Theory

    摘要
  • 摘要: 为提高铁路桥梁动力可靠度计算的效率,考虑结构非线性,基于振型空间,导出了铁路桥梁动能和势能的表达式,进而根据拟Hamilton系统理论确定铁路混凝土桥梁的广义动量、广义速度、Hamilton函数及拟Hamilton系统方程.只考虑横向位移和扭转位移,导出了铁路混凝土桥梁的拟不可积Hamilton系统方程,得到条件可靠度函数应满足的后向Kolmogorov方程及其定量边界、初值条件,并用中心差分法求解该方程.以实际铁路桥梁为算例,用上述方程求解其在列车荷载作用下的动力可靠度.研究结果表明:非线性桥梁结构的动力可靠度和概率密度峰值随桥梁初始能量增大而减小,随桥梁临界能量增大而增大;不同跨度桥梁的分析结果与实际情况相符,说明基于拟不可积Hamilton系统理论计算铁路桥梁的非线性动力可靠度是可行的.

     

    Abstract: To improve the computation efficiency of bridge dynamic reliability, kinetic energy and potential energy of a railway bridge with nonlinear characteristics were expressed in the modal space, and the generalized momentum, the generalized velocity, the Hamiltonian function and the quasi-Hamiltonian system equation were established based on the quasi-Hamiltonian system theory. A quasi-non-integrable-Hamiltonian equation for a railroad concrete bridge was derived just considering its lateral and torsion displacements, and the backward Kolmogorov (BK) equation governing conditional reliability function and its corresponding quantitative boundary and initial conditions were obtained, and the central finite difference method was introduced to calculate the BK equation. The case research results show that the dynamic reliability of a nonlinear bridge structure and the peak value of probability density decrease as the primary energy increases, while they increase as the limit energy raises; and the contrastive analysis results of railway bridges with different spans are agreed with the actual situations, illustrating that the dynamic reliability calculation of railway bridges based on the quasi-non-integrable-Hamiltonian system theory is feasible.

     

    • HTML全文
    • 参考文献(22)
  • 曾庆元,郭向荣. 列车桥梁时变系统振动分析理论与应用[M]. 北京:中国铁道出版社,1999: 1-14.
    郭文华,曾庆元. 高速铁路多跨简支梁桥横向振动随机分析[J]. 长沙铁道学院学报,1997,15(1): 1-9. GUO Wenhua, ZENG Qingyuan. Transverse random vibration analysis for the high-speed railway multi-span simply-supported bridge[J]. Journal of Changsha Railway University, 1997, 15(1): 1-9.
    刘佩. 随机地震作用下结构动力可靠度计算方法研究[D]. 北京:北京交通大学土木建筑工程学院,2010.
    LI J, CHEN J B. Stochastic dynamics of structures[M]. New York: John Wiley and Sons, 2009: 191-308.
    CHEN J B, LI J. A note on the principle of preservation of probability and probability density evolution equation[J]. Probabilistic Engineering Mechanics, 2009, 24: 51-59.
    RICE S O. Mathematical analysis of random noise[J]. Bell System Technical Journal, 1944, 23(3): 282-332.
    RICE S O. Mathematical analysis of random noise[J]. Bell System Technical Journal, 1945, 24(1): 146-156.
    朱位秋. 非线性随机动力学与控制:Hamilton理论体系框架[M]. 北京:科学出版社,2004: 1-369.
    ZHU W Q, CAI G Q. Random vibration of viscoelastic system under broad-band excitations[J]. International Journal of Non-Linear Mechanics, 2011(46): 720-726.
    ZHU W Q, CAI G Q. Generation of non-Gaussian stochastic processes using nonlinear filters[J]. Probabilistic Engineering Mechanics, 2014, 36: 56-62.
    HU R C, YING Z G, ZHU W Q. Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle[J].Structural and Multidisciplinary Optimization, 2014(49): 69-80.
    GAN C B, ZHU W Q. First-passage failure of quasi-non-integrable-Hamiltonian systems[J]. International Journal of Non-Linear Mechanics, 2001(36): 209-220.
    ZENG Y, ZHU W Q. Stochastic averaging of quasi-nonintegrable-Hamiltonian systems under Poisson white noise excitation[J]. ASME Journal of Applied Mechanics, 2011, 78(2): 021002-021011.
    GU X D, ZHU W Q. Stochastic optimal control of quasi non-integrable Hamiltonian systems with stochastic maximum principle[J]. Nonlinear Dynamics, 2012, 70: 779-787.
    GU X D, ZHU W Q. Optimal bounded control of quasi-nonintegrable Hamiltonian systems using stochastic maximum principle[J]. Nonlinear Dynamics, 2014, 76: 1051-1058.
    CHOPRA A K. Dynamics of structures: theory and applications to earthquake engineering[M]. New Jersey: Prentice Hall, 1995: 409-429, 659-683.
    赫中营. 基于拟Hamilton理论的既有铁路桥梁动力可靠度研究[D]. 兰州:兰州交通大学土木工程学院,2008.
    陈滨. 分析动力学[M]. 北京:北京大学出版社,1987: 401-406.
    星谷胜. 随机振动分析[M]. 常宝琦,译. 北京:地震出版社,1977: 143-163.
    陆金甫. 偏微分方程差分方法[M]. 北京:高等教育出版社,1988: 191-272.
    严隽耋. 车辆工程[M]. 北京:中国铁道出版社,2003: 275-336.
    刘卫国. MATLAB程序设计教程[M]. 北京:中国水利水电出版社,2005: 152-206.
    • 相关文章
    • 施引文献
  • 附加材料(0)
  • 加载中
WeChat 点击查看大图
计量
  • 文章访问数:  782
  • HTML全文浏览量:  63
  • PDF下载量:  400
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-12-15
  • 刊出日期:  2016-01-25

目录

    /

    返回文章
    返回

    Copyright © 2009 西南交通大学学报

    地址：四川省成都市郫都区犀安路999号西南交通大学犀浦校区《西南交通大学学报》编辑部

    电话：028-66367562传真：028-66366552Email：xbz@home.swjtu.edu.cn

    本系统由 北京仁和汇智信息技术有限公司 开发 技术支持： info@rhhz.net