弹性接触下车辆—变截面梁桥竖向振动分析

Vertical Vibration of Non-Uniform Continuous Bridge Travelled by Vehicle Considering Elasticity Contact

基于Hertz弹性接触理论,分别推导了变截面梁单元和车辆动力方程,然后根据分析目的提出了系统方程组装和求解思路,解决了传统分析中"车轮密贴"假设和结构简单的不足。新方法系统质量和阻尼矩阵不再时变,采用Newmark-β方法直接求解,不需迭代,并采用自动半步长法准确确定接触状态发生改变时刻。数值算例表明,新方法能更为精细分析系统动力响应,并能准确模拟脱离现象。应用新方法分析了两种不同车辆模型对耦合系统动力响应的影响,结果表明:整车模型能直接准确获得车辆动力响应;若采用集总车辆模型,可采用将其前后两簧上质量加速度平均的方法近似评估车体加速度。

Based on Hertz contact theory, the motion equations for non-uniform continuous bridge andvehicle are separately established, and the processes for assembling and solving the system equations are proposed. The proposed method can be used for complicated structure, and the deficiency of the no-jump assumption is improved. Without iterative, the Newmark＇s β integration method is adopted to solve the couple equations, and the half step algorithm is adopted to determine the occurrence time of transient jump. The numerical example demonstrates that the proposed method is more suitable for the precise analysis and can simulate the transient jump. The effect of two different vehicle models to the dynamic response is studied. The results demonstrate that the whole vehicle model can directly get the dynamic response while the average of the two sprung mass accelerations can be used to evaluate the acceleration of the car body for the lumped vehicle model.