车辆作用下中小跨径裂缝简支梁桥自振特性分析

Free vibration analysis of a small or medium-span cracked simply supported bridge considering bridge-vehicle interaction

基于传递矩阵方法的基本思想,形成了车辆作用下裂缝简支梁桥自振特性的分析方法。在确定了简支梁桥及车辆简化模型的基础上,首先明确了表征梁体振动形状的待定系数在裂缝间的传递关系,接着从结构振动的基本原理出发,建立了车轮处梁体待定系数方程和表征车辆振动的待定系数方程。其次采用数值组装方法把车轮处的待定系数方程、车辆振动待定系数方程以及边界条件组合成了一个新型的车辆-裂缝简支梁耦合体系自由振动方程,通过求解该方程便可得到车辆作用下裂缝简支梁桥的自振特性。最后采用多种工况下的数值模拟计算来验证该方法的正确性和有效性。

A method for free vibration characteristics analysis of a cracked simply supported bridge with vehicles is proposed by using the transfer matrix method. The simplified models of the simply supported bridge and vehicle are established, based on which the transitive relations of the undetermined coefficients representing vibration shapes among cracks are presented. The undetermined coefficient equations of beams and vehicles are obtained by the basic principle of structural vibration. Then, the numerical assembling method is utilized to obtain a new free vibration equation for the coupled system of vehicles and cracked simply supported beams, which is a function of the boundary conditions and the undetermined coefficients of beams and vehi- cles. The free vibration characteristics of a cracked simply supported bridge with vehicles can be obtained by solving the free vi- bration equation. Finally, various numerical examples are provided to validate the presented method. The results are in good a- greement with those obtained by finite element method. In the article, a study to investigate the effect of vehicles or cracks on the natural frequencies of the bridge is conducted.