车桥耦合振动理论在桥面不平度研究中的应用
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摘要
将车桥系统视为两个分离的子系统,应用达朗贝尔原理推导了双轴密贴车辆模型和桥梁的运动平衡方程,采用分离迭代法对车桥振动问题进行数值求解。利用MATLAB结合NWMARK法计算原理编制了车桥耦合计算程序,对该程序的准确性进行了验证,在此基础上研究了桥面状况和车速对车桥振动的影响。结果表明:该程序的计算结果准确可靠,桥面状况对车桥振动影响很大,车速对桥梁振动的影响取决于与其对应的车辆对桥梁作用力的频率。
The vehicle-bridge system are considered as two separate subsystems,and the vibration equilibrium functions for double axis vehicle model and bridge are derived with the application of d'Alembert principle.And then the separate iteration method is applied in the numerical solution of vehicle-bridge coupling vibration problem.In consideration of NEWMARK numerical calculation principals,computational procedures for vehicle-bridge coupling vibration are compiled by use of MATLAB.Furthermore,the accuracy of this program is verified.The influence of the deck conditions and vehicle speed on vehicle-bridge system is discussed on the basis of this program.It demonstrates that the solution is accurate and the influence of the deck conditions on vehicle-bridge vibration is significant;the influence of the vehicle speed on bridge vibration depends on the force frequency caused by vehicle on the bridge.
The vehicle-bridge system are considered as two separate subsystems,and the vibration equilibrium functions for double axis vehicle model and bridge are derived with the application of d'Alembert principle.And then the separate iteration method is applied in the numerical solution of vehicle-bridge coupling vibration problem.In consideration of NEWMARK numerical calculation principals,computational procedures for vehicle-bridge coupling vibration are compiled by use of MATLAB.Furthermore,the accuracy of this program is verified.The influence of the deck conditions and vehicle speed on vehicle-bridge system is discussed on the basis of this program.It demonstrates that the solution is accurate and the influence of the deck conditions on vehicle-bridge vibration is significant;the influence of the vehicle speed on bridge vibration depends on the force frequency caused by vehicle on the bridge.
引文
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[8]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,2002,24(5):113-120.Li Xiaozhen,Qiang Shizhong.State of the art review and trend ofstudies on vehicle-bridge interaction[J].Journal of the ChinaRailway Society,2002,24(5):113-120.
[9]Chopra A K.结构动力学理论及其在地震工程中的应用[M].2版.谢礼立,吕大刚,译.北京:高等教育出版社,2005:124-127.Chopra A K.Dynamics of Structure Theory and Application toEarthquake Engineering[M].2nd ed.Xie Lili,Lv Dagang,trans.Beijing:Higher Education Press,2005:124-127.
[10]Bathe K J,Wilson E l.Solution methods for Eigen value problemsin structural mechanics[J].International Journal for NumericalMethods in Engineering,1973,6(2):213-226.
[2]Gillespie T D.车辆动力学基础[M].赵六奇,金达锋,译.北京:清华大学出版社,2006.Gillespie T D.Fundamentals of Vehicle Dynamics[M].Zhao Li-uqi,Jin Dafeng,trans.Beijing:Tsinghua University Press,2006.
[3]陈炎,黄小清,马友发.车桥系统的耦合振动[J].应用数学与力学,2004,25(4):354-358.Chen Yan,Huang Xiaoqing,Ma Youfa.Coupling vibration of vehi-cle-bridge system[J].Applied Mathematics and Mechanics,2004,25(4):354-358.
[4]曹雪琴,刘必胜,吴鹏贤.桥梁结构动力分析[M].北京:中国铁道出版社,1987:60-90.Cao Xueqin,Liu Bisheng,Wu Pengxian.Dynamic Analysis ofBridge Structure[M].Beijing:China Railway Publishing House,1987:60-90.
[5]卜建清,娄国充,罗韶湘.汽车对桥梁冲击作用分析[J].振动与冲击,2007,26(1):52-64.Bu Jianqing,Lou Guochong,Luo Shaoxiang.Analysis on impacteffects of bridge due to moving vehicle[J].Journal of Vibrationand Shock,2007,26(1):52-64.
[6]徐昭鑫.随机振动[M].北京:国防工业出版社,1990.Xu Zhaoxin.Random Vibration[M].Beijing:National Defense In-dustry Press,1990.
[7]韩万水.风-汽车-桥梁系统空间耦合振动研究[D].上海:同济大学,2006.Han Wanshui.Three-Dimensional Coupling Vibration of Wind Ve-hicle Bridge System[D].Shanghai:Tongji University,2006.
[8]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,2002,24(5):113-120.Li Xiaozhen,Qiang Shizhong.State of the art review and trend ofstudies on vehicle-bridge interaction[J].Journal of the ChinaRailway Society,2002,24(5):113-120.
[9]Chopra A K.结构动力学理论及其在地震工程中的应用[M].2版.谢礼立,吕大刚,译.北京:高等教育出版社,2005:124-127.Chopra A K.Dynamics of Structure Theory and Application toEarthquake Engineering[M].2nd ed.Xie Lili,Lv Dagang,trans.Beijing:Higher Education Press,2005:124-127.
[10]Bathe K J,Wilson E l.Solution methods for Eigen value problemsin structural mechanics[J].International Journal for NumericalMethods in Engineering,1973,6(2):213-226.
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