车桥耦合系统随机振动的时域显式解法

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.

Random Vibration Analysis of Coupled Vehicle-Bridge Systems With the Explicit Time-Domain Method

The vibration of coupled vehicle-bridge systems subjected to random deck or track irregularities exhibits typical non-stationary stochastic features. The explicit expressions for the dynamic responses of the vehicle and the bridge subsystems were first established. Based on the motion compatibility condition between the vehicle and the bridge, the explicit expression for the vehicle-bridge contact force in terms of deck irregularities was then derived. Such explicit formulation reflects the physical evolution mechanism of the coupled vehicle-bridge system. Subsequently, the evolutionary statistical moments of the vehicle-bridge contact force were obtained through direct application of the statistical moment operation rules, thereafter the evolutionary statistical moments for critical responses of the vehicle and the bridge subsystems could be calculated. In addition, a random simulation method (i.e. the Monte Carlo simulation method) was put forward based on that the contact force was explicitly expressed in terms of deck irregularities. In turn, the evolutionary statistical moments or the other statistical properties of the critical responses of the coupled vehicle-bridge system could be easily achieved. Since the physical and probabilistic evolution processes of the coupled system were coped with in a relatively separate manner, the proposed method avoided repeated solution of the motion equations for the system. Moreover, a dimension-reducing scheme was involved for the calculation of the statistical moments of the contact force and other related responses as well. All these merits enable the proposed method to be more effective for random vibration analysis of coupled vehicle-bridge systems, as compared with the previous methods. Numerical examples indicate that the proposed method has high accuracy and superior computational efficiency.