简支梁桥有载频率分析

根据桥梁固有频率的定义求解桥梁振动微分方程，给出了列车荷载作用下简支梁桥有载频率的解析表达式．研究表明，桥梁有载频率与其上作用车辆的简化模型、过桥车辆数、行车速度以及桥梁跨度等有关：1辆车简化为4个或2个轮对时，桥梁有载频率很接近，比较符合实际情况；车辆总长超过桥梁跨度时，桥梁有载频率呈稳定的周期性变化；桥梁有载频率随时间变化，与车辆在桥上的位置有关，且行车速度越快，频率变化越快。

Analysis of Loaded Frequency of Simply-Supported Beam Bridge

Based on the definition of natural bridge frequency, the analytical expression of loaded frequency of a simply-supported beam bridge under train loads was given through solving the vibration differential equation for bridges . The research shows that the loaded frequency of a bridge is in relation to the simplified models of a vehicle, the number of vehicles passing the bridge, train speed, bridge span and so on. The loaded frequency obtained is very proximate to the actual value when a vehicle is simplified as 4 or 2 wheelsets. It varies periodically when the total length of a train is larger than the bridge span. Furthermore, the loaded bridge frequency changes with time, relative to the location of vehicles on a bridge, and the faster a train moves, the more quickly the frequency varies.