车桥耦合系统随机振动的时域显式解法

发布时间：2018-06-20 08:03

本文选题：车桥耦合 + 桥面不平顺　；参考：《应用数学和力学》2017年01期

【摘要】：在桥面和轨道随机不平顺作用下,车桥耦合系统振动是一个典型的非平稳随机振动问题.笔者分别建立表征物理演变机制的车辆系统和桥梁系统的动力响应显式表达式,然后利用车桥之间的运动相容条件,建立车桥之间接触力关于桥面不平顺的显式表达式.在此基础上,即可直接利用统计矩运算法则,获得车桥接触力的统计矩演化规律,并进一步计算车辆系统和桥梁系统关键响应的演变统计矩.此外,也可以基于车桥接触力关于桥面不平顺的显式表达式,高效地进行随机模拟(即Monte Carlo模拟,MCS),以获得车桥耦合系统关键响应的演变统计矩及其他统计信息.在上述过程中,由于实现了车桥耦合系统物理演变机制和概率演化规律的相对分离,在响应统计矩计算中,无需反复求解车桥耦合系统的运动微分方程,且可以仅针对车桥接触力及其他所关注的关键响应开展降维计算,大幅提高了车桥耦合系统随机振动的计算效率.数值算例表明,所提出的方法具有理想的计算精度和计算效率.
[Abstract]:Under the action of random irregularity of bridge deck and track, the vibration of vehicle-bridge coupling system is a typical non-stationary random vibration problem. The explicit expressions of the dynamic response of vehicle system and bridge system which represent the mechanism of physical evolution are established respectively. Then the explicit expression of the contact force between the vehicle and the bridge for the bridge deck irregularity is established by using the motion compatibility condition between the vehicle and the bridge. On this basis, the statistical moment evolution law of vehicle-bridge contact force can be obtained directly by using statistical moment algorithm, and the evolving statistical moments of critical response of vehicle system and bridge system can be further calculated. In addition, based on the explicit expression of bridge contact force on bridge deck irregularity, the stochastic simulation (i.e. Monte Carlo simulation) can be carried out efficiently to obtain the evolution statistical moments and other statistical information of the critical response of vehicle-bridge coupling system. In the above process, due to the relative separation of physical evolution mechanism and probability evolution law of vehicle-bridge coupling system, there is no need to repeatedly solve the kinematic differential equation of vehicle-bridge coupling system in response statistical moment calculation. Furthermore, the dimensionality reduction calculation can only be carried out for the vehicle-bridge contact force and other key responses concerned, which greatly improves the efficiency of random vibration calculation of the vehicle-bridge coupling system. Numerical examples show that the proposed method has ideal accuracy and efficiency.
【作者单位】：华南理工大学土木与交通学院;亚热带建筑科学国家重点实验室(华南理工大学);
【分类号】：O324;;U441+.3

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