摘要：为了研究中下承式拱桥在公路车辆作用下的吊杆冲击系数不均匀性问题，提出了基于车桥耦合振动的公路
桥梁动力响应分析方法。首先，将车辆简化为4 个自由度的整车模型，根据D'Alembert 原理推导了车辆振动方程，
将桥梁离散为二维有限元模型，根据车辆与桥梁接触点处位移与力的协调条件耦合二者的振动方程；然后，采用
Newmark-β 算法，基于MATLAB 语言编制了公路桥梁车桥耦合振动计算程序VBAP；最后，以某钢管混凝土拱
桥为例，利用本文方法与程序分析了结构阻尼、桥上路面粗糙度、车重及车速对吊杆应力冲击系数的影响。

Abstract: In order to investigate the stress impact factor difference of the suspenders on the half-through or though
arch bridge under the dynamic loading of road vehicles, the vehicle-bridge vibration based analysis method is proposed.
Firstly, the vehicle is modeled as a four-degree-of-freedom system and the vibration equations of the vehicle modal are
deduced based on the D'Alembert principle. Then finite element method is used to discretize bridge and a 2D finite
element modal is set up. According to the condition of displacement and force compatibility between vehicle and bridge,
the vibration equations of vehicle modal and bridge modal are coupled. Secondly, a professional procedure VBAP is
programmed based on Newmark-β algorithm in MATLAB, which could analyze the vehicle-bridge system coupling
vibration. At last, taking one concrete-filled steel tube arch bridge as an example, the influence of damping ratio, road
roughness class, the weight of vehicle and vehicle speed on stress impact factors of the suspenders is analysed using
method and program mentioned in this paper.