任意移动荷载列作用下简支梁桥竖向振动响应解析分析

Vertical dynamic response analysis of a simply supported beam bridge under successive moving loads

采用振动理论推导欧拉-贝努利梁在任意移动荷载列模型作用下其竖向振动的解析表达式。在表达式中综合考虑列车移动速度、所选取的振型阶数、简支梁自身的质量和刚度以及体系的阻尼比对简支梁竖向动力响应的影响。并用MATLAB语言编程计算,对结果的正确性进行校核。以京沪高速线路上32 m简支梁桥为例,分析简支梁桥在8辆ICE3动车编组的荷载列作用下的竖向动力响应。计算结果表明,该方法能够模拟桥梁在间距、大小均任意的移动荷载列作用下的竖向振动。解析结果应用于高速铁路的初步设计及对最大振动能级进行评估时可快速得出可靠结果。

Here,the vibration theory was used to deduce vertical vibration＇s analytical expressions of an Euler-Bernoulli beam under sucessive moving loads.In the analytical expressions,the influences of the train＇s speed v,the number of vibration modes selected n,the beam mass m,the rigidity EI of the beam and the damping ratio ξn of the system on the vertical dynamic response of a simply supported beam bridge were considered comprehensively.Then,the calculating program was made with MATLAB to analyze the dynamic response of a bridge in an example so as to check the correctness of the analytical expressions.A 32-meter long simply supported beam bridge of Beijing-Shanghai high-speed railway was taken as a typical example.Its vertical vibration under the moving loads of 8 ICE3 motor car groups was calculated and the properties of the vibration response were analyzed.The calculation results showed that the proposed method can be used to compute the vertical vibration of a beam subjected to randomly spaced loads;the analytical expressions are applicable to railway bridge preliminary design and assessment of the expected maximum vibration levels under high-speed trains passing;the reliable results are obtained rapidly.