| 基于拟不可积哈密顿理论的桥梁动力可靠度计算 |
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| 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. |
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| 作者姓名： | 赫中营 王根会 叶爱君 夏修身 |
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| 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) |
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| 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.
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| 关 键 词： | 铁路桥梁 动力可靠度 拟不可积Hamilton系统理论 有限差分法 |
| 收稿时间： | 2014-12-15 |
Dynamic Reliability Calculation of Bridge Based on Quasi-non-integrable-Hamiltonian System Theory |
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| 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. |
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| Authors: | HE Zhongying WANG Genhui YE Aijun XIA Xiushen |
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| 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. |
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