车桥耦合系统随机振动的时域显式解法

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.