车桥耦合振动迭代求解稳定性研究  

Numerical stability of iterative scheme in solving coupled vibration of a train-bridge system

作　　者：杜宪亭[1] 夏禾[1] 张田[1] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044

出　　处：《振动与冲击》2012年第22期62-65,70,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(51208027;51178025);973计划(2013CB036203);中央高校基本科研业务费项目(C11JB00540)

摘　　要：将桥梁、车辆分别简化为竖向振动的弹簧振子、簧上质量系,应用谱半径理论研究不同轮轨关系、不同迭代格式下车桥动力相互作用的数值求解稳定性问题,针对可能引起迭代计算发散的原因,提出改进措施。研究表明,采用轮轨分离模型,时间积分步足够小,迭代过程即可收敛;轮轨密贴分析模型中,轮对质量大于所通过桥梁节点质量时采用直接迭代格式会造成数值计算发散;轮轨密贴模型迭代求解过程中应用该虚拟质量法既可避免迭代数值发散亦可保留直接迭代优点。Bridge and vehicle subsystems were simplified into oscillators connected with springs or a system of masses with springs in vertical direction, respectively. The numerical stabilities of iterative schemes in solving dynamic interaction of train and bridge were studied with different wheel-rail relations on the basis of the spectral radius theory. The corresponding improvement approach was proposed in term of possible causes leading to numerical divergence. The results showed that the iteration can converge if the time step is small enough for the wheel-rail separation model; for the wheel-rail non-separation model, direct iterative scheme may lead to numerical instability if the mass of a bridge node is smaller than that of the passing wheel-pair; the virtual mass approach is proposed, it can not only avoid potential divergence but also retain the advantages of direct iterative scheme.

关 键 词：车桥系统 轮轨关系 迭代格式 数值稳定性 谱半径 

分 类 号：U24[交通运输工程—道路与铁道工程]