基于拟可积Hamilton系统的铁路桥梁动力可靠度计算研究

Research on Calculation of Dynamic Reliability of Existing Railway Bridge Based on Quasi-Integrable-Hamiltonian Theory

铁路运输提速增载,迫切需要对铁路桥梁动力可靠度进行研究。本文基于振型空间,首先推导出结构体系的广义动能和势能,继而基于拟Hamilton系统理论,推导出铁路混凝土桥梁的拟可积Hamilton系统方程。只考虑横向和扭转位移,得到铁路混凝土桥梁的条件可靠性函数所满足的BK方程及其定量边界、初值条件,可用中心差分法进行求解。以实际桥梁为算例,用上述方程求解其在列车荷载下的动力可靠度,得出或验证了与实际情况相符的若干重要结论,结果表明:动力可靠度和概率密度峰值,随桥梁初始能量的增大而减小,随桥梁边界能量的增大而增大;不同跨度桥梁分析结果与实际情况相符,说明基于拟可积Hamilton系统理论计算铁路桥梁的动力可靠度是可行的。

Due to faster speed and heavier load of railway transportation,there is a pressing need to study dy-namic reliability of railway bridges.In this paper,the generalized kinetic energy and potential energy expres-sions were first deduced in the mode shape space for structural system.Further,based on the Quasi-Hamilto-nian system theory,the Quasi-Integrable-Hamiltonian system equation for railway concrete bridges was estab-lished in the mode space.With only the lateral and torsional displacements of railway bridges being considered, the backward Kolmogorov equation governing conditional reliability function has been obtained with its corre-sponding quantitative boundary and initial conditions,which can be solved by the central finite-difference meth-od.In the case of actual bridges,the above equation was used to calculate dynamic reliability of exited railway PC bridges under dynamic train load.Some important conclusions that agreed with the actual situation were drawn and verified.The results showed that the dynamic reliability and peak value of probability density de-creased with the increase of the primary energy of the bridge and increased with the increase of the boundary energy of the bridge.The results of the contrastive analysis of railway bridges with different spans were con-sistent with the actual situation,proving the feasibility to calculate the dynamic reliability for railway bridges using the Quasi-Integrable-Hamiltonian system theory.