本文通过Galerkin方法对经典的悬索桥垂向弯曲振动方程进行离散,得到了包含三个二阶方程的常微分组.通过该常微分方程组的解析解,研究了车过载荷作用下结构的动力学行为,并和有限元计算结果进行对比.研究结果显示,Galerkin方法得到的一阶、二阶振动频率和有限元结果一致,但三阶模态的振动频率比有限元的结果大;车过载荷作用下,三阶模态截断得到的解析解在整体运动趋势和有限元计算结果一致.因此,要较精确的描述悬索桥的动力学行为,需要考虑二阶和三阶模态.%In this paper, a system of second order ordinary differential equations (ODEs) is obtained through applying Galerkin method in the classical mathematical model of bending vibration of the suspension bridges. The ODEs, which include three equations, are used to describe the vibrations of the bridge for the vehicle loads. By comparing the analysis solutions of the ODEs with the solutions of finite element, the conclusions can be found as follow: ①the first two analytical frequencies are good agree with the finite element one, but the third analytical frequency is greater than the finite element one about 10%; ②for the vehicle loads, the analytical solutions describe appropriately the entirety motion. Therefore, when the oscillations of the bridge are researched, it is necessary to take the second and third order modal into account.
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