移动简谐荷载列作用下简支梁竖向动力响应的解析解及其应用研究

Analysis and application of vertical dynamic response of simply supported beam bridge under moving harmonic load series

基于移动简谐荷载列模型,理论推导了简支梁竖向动力响应的解析表达式;利用该解析式编写MATLAB程序,对CRH3动车组作用下的高速铁路32m标准简支梁进行了竖向共振分析,研究了谐振频率、荷载列移动速度、体系阻尼比等因素对共振效应的影响。计算结果表明:阻尼比减振效果随阻尼比的增大而减弱,故结构设计中不宜过度提高阻尼比;在阻尼比为0.02时,谐振频率引起共振的动力放大系数超过20,而过桥速度引起的共振动力放大系数最大仅约为2.5,但考虑到前者对应的荷载幅值仅为后者对应荷载值的0.2,故建议在实际设计中应充分考虑两种情况下的共振效应。最后通过与已有文献结果的对比,验证了该解析推导结果的正确性。本文解析式能够直接迅速地进行参数影响分析,为初步设计提供了参考。

Based on the model of moving harmonic load series, the analytical expression of vertical dynamic response of simple supported beam has been derived and then verified through comparing with results of other different calculation methods. Vertical resonance of 32m standard high-speed railway simple supported beam has been studied using the analytical expression and MATLAB programs under the action of CRH3 train formation.Effects of frequency, velocity of moving load series and damping ratio of structure system on resonance have also been studied. Calculation results show that the damping effect becomes weaker with the increasing of damp ratio,thus the value of damp ratio should not be too high in structural design. With a damp ratio of 0.02, the dynamic magnification factor of harmonic resonance exceeds 20, while that of resonance induced by velocity is only 2.5 at most. But given that the former load magnitude is only 0.2 of the later one, both magnification effects should be fully considered in practical design. Analysis of resonance effect indicates that helping analyze parameters directly and quickly, the analytical expression in this paper is reliable and can be referred to in preliminary design.