车辆-轨道-桥梁竖直耦合振动程序设计及仿真
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摘要
为研究轨道交通车辆经过高架桥时的动态特性,以弹性支承块式无砟轨道为例,基于车辆-轨道耦合动力学理论,建立了车辆-轨道-桥梁耦合系统的竖向振动矩阵方程,利用MATLAB软件编写了计算程序。数值算例验证了计算程序的可靠性。通过改变系统参数,探索了轨道不平顺、车辆速度和轨道结构竖向刚度对系统竖向振动响应的影响。结果表明:轨道振动频率分布在0~500 Hz范围内,以20 Hz以内的低频振动为主;桥梁振动频率分布在0~200Hz范围内,以一阶竖向弯曲振动为主;轨道不平顺所产生的轮轨高频冲击力可达轴重的3倍,是车辆-轨道-桥梁耦合系统重要激励源之一;轮轨力和轨道加速度响应对车速的变化敏感,车辆-轨道-桥梁耦合系统位移响应对车速的变化不敏感;扣件和支承块胶垫竖向刚度应根据设计要求在40~80 k N/mm之间进行合理匹配取值。
To study the dynamic performance of elastic supporting block track when the train runs on the viaduct,ballastless track with elastic supporting block is taken as the example,and based on vehicle-track coupling dynamics theory,a matrix equotian for vehicle-track-bridge vertical coupling vibration is built and a programis designed on MATLAB software. A numerical example verifies the reliability of the program. By changing the systemparameters,the influences of vehicle speed,track vertical stiffness and track irregularity on the systemvertical vibration responses are investigated. Results showthat the frequency distributions of track and bridge are between 0 ~ 500 Hz,the main vibration frequencies of track are bellow20 Hz while the bridge is centered on first-order vertical bending vibration bwtween 0 ~ 200 Hz. Track irregularity is an important source of excitation to the system,and the impact force can reach to 3times bigger than of axle load due to the irregularity. Wheel / rail force and track acceleration responses are more sensitive to the change of vehicle speed than the displacement responses. So the vertical stiffness of rail fastener and block pad should match each other and be valued between 40 ~ 80 k N / mmaccording to the design requirements.
To study the dynamic performance of elastic supporting block track when the train runs on the viaduct,ballastless track with elastic supporting block is taken as the example,and based on vehicle-track coupling dynamics theory,a matrix equotian for vehicle-track-bridge vertical coupling vibration is built and a programis designed on MATLAB software. A numerical example verifies the reliability of the program. By changing the systemparameters,the influences of vehicle speed,track vertical stiffness and track irregularity on the systemvertical vibration responses are investigated. Results showthat the frequency distributions of track and bridge are between 0 ~ 500 Hz,the main vibration frequencies of track are bellow20 Hz while the bridge is centered on first-order vertical bending vibration bwtween 0 ~ 200 Hz. Track irregularity is an important source of excitation to the system,and the impact force can reach to 3times bigger than of axle load due to the irregularity. Wheel / rail force and track acceleration responses are more sensitive to the change of vehicle speed than the displacement responses. So the vertical stiffness of rail fastener and block pad should match each other and be valued between 40 ~ 80 k N / mmaccording to the design requirements.
引文
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[3]张志超,张亚辉,林家浩.车桥耦合系统非平稳随机振动分析的虚拟激励-精细积分法[J].工程力学,2008(11):197.
[4]逄焕平,董满生,侯超群.车桥耦合振动分析的状态空间法[J].合肥工业大学学报:自然科学版,2012(12):1610.
[5]罗文俊,雷晓燕,练松良.车辆-高架桥耦合系统竖向振动分析车辆轨道新模型[J].华东交通大学学报,2013(2):1.
[6]李东平,王宁波,曾庆元.车桥时变系统耦合振动分析模态综合法[J].铁道科学与工程学报,2009(3):36.
[7]Vo T P,Lee Jaehong,Ahn N.On sixfold coupled vibrations of thin-walled composite box beams[J].Composite Structures,2009(89):524.
[8]Nallasivam K,Dutta A,Talukdar S.Dynamic analysis of horizontally curved thin-walled box-girder bridge due to moving vehicle[J].Shock and Vibration,2007(14):229.
[9]Wu S Q,Law S S.Dynamic analysis of bridge-vehicle system with uncertainties based on the finite element model[J].Probabilistic Engineering Mechanics,2010(25):425.
[10]翟婉明.车辆轨道耦合动力学[M].北京:中国铁道出版社,1997.
[11]王宁波,任伟新,肖祥.列车-桥梁耦合振动研究综述[J].力学进展,2012(5):634.
[12]Uzzal R U A,Ahmed A K W,Rakheja S.Analysis of pitch plane railway vehicle-track interactions due to single and multiple wheel flats[J].Proceedings of the Institution of Mechanical Engineers,2009(1):375.
[13]杜宪亭,夏禾,张田.车桥耦合振动迭代求解稳定性研究[J].振动与冲击,2012(22):62.
[14]Zhua J J,Ahmed K W,Rakhej S,et al.Development of a vehicletrack model assembly and numerical method for simulation of wheel-rail dynamic interaction due to unsupported sleepers[J].Vehicle System Dynamics:International Journal of Vehicle Mechanics and Mobility,2010(12):1535.
[15]李永乐.风-车-桥系统非线性空间耦合振动研究[D].成都:西南交通大学,2003.
[16]Lou Ping,Yu Zhiwu,Au F T K.Rail-bridge coupling element of unequal lengths for analyzing train-track-bridge interaction systems[J].Applied Mathematical Modelling,2012(36):1395.
[17]李小珍,强士中.列车-桥梁耦合振动研究的现状与发展趋势[J].铁道学报,2002(5):112.
[18]徐荣桥.结构分析的有限元法与MATLAB程序设计[M].北京:人民交通出版社,2005.
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