考虑墩体参振的高速磁浮交通轨道梁动力特性研究
|
摘要
在高速磁浮列车作用下,轨道梁、墩会发生较大的变形和振动,对结构的安全、车辆的运行安全以及旅客的乘坐舒适度会产生很大的影响。针对磁浮系统的车桥振动,到目前为止的研究工作,无论是对连续梁还是简支梁,鲜少考虑墩的作用。随着墩的升高,墩的刚度会影响整个结构体系的动力特性,成为不可忽略的因素。高速磁浮列车引起的梁墩体系动力问题已成为当前高速磁浮技术发展遇到的重要课题。
本文结合国家自然科学基金资助项目《高速磁浮交通轨道梁动力特性研究》(项目号:50578010)的研究工作,建立了考虑墩体参振的高速磁浮列车-轨道梁系统动力分析模型,在电磁相互作用和梁墩体系自振特性分析的基础上,以磁浮线路实测不平顺作为外界激励源,对高速磁浮列车运行时所引起的车辆、轨道梁、墩的各项动力响应进行了计算分析,得出了高速磁浮列车引起的梁墩体系动力响应基本规律,从而为高速磁浮梁墩参数选取和方案选择提供理论基础与参考建议。全文具体开展了如下几方面的研究工作:
(1)分析了高速磁浮列车、轨道梁、墩系统的电磁学、力学耦合关系,运用结构动力学、车辆动力学及电磁控制理论原理,采用模态综合技术,建立了考虑墩体参振的高速磁浮列车-轨道梁系统动力分析模型,给出了具体求解步骤。基于本文的分析理论以及多年的科研积累,独立编制了车-梁-墩动力分析程序。通过现场试验结果验证理论模型和分析方法的有效性。
(2)分析了磁浮线路平纵横面和线路结构主要特点,介绍了磁浮系统参数、轨道梁和下部结构相关技术要求,对乘坐舒适度控制指标、轨道梁及下部结构相关技术要求和参数选定依据和影响因素进行了综合分析,并和高速铁路相关标准进行了对比研究,为梁墩体系动力性能评价提供了评判标准。
(3)建立了电磁相互作用数学模型,研究了控制方案、控制参数、轨道梁参数对悬浮性能的影响规律,确定了保证高速磁浮列车稳定悬浮的磁轨参数匹配关系,提出了控制悬浮阶段过大振动的原则。
(4)以工程实践为背景,建立了磁浮交通轨道梁墩体系有限元模型,采用子空间迭代法计算了梁墩体系特征值和模态,分析了不同梁型、约束、墩高、墩重、跨数等因素对梁墩体系自振特性的影响,阐明了恒载作用下轨道梁墩体系动力特性,为进一步分析高速磁浮列车作用下梁墩体系动力响应及运行安全性和舒适性奠定基础。
(5)采用车-梁-墩动力相互作用模型,以磁浮线路实测不平顺作为外界激励源,对高速磁浮列车运行时所引起的车辆、轨道梁、墩的各项动力响应进行计算分析,研究了梁墩体系垂向共振和横向共振条件,对简支梁和两跨连续梁进行了动力学性能分析评估,阐明了高速磁浮列车作用下轨道梁墩体系动力特性。图119幅,表20个,参考文献138篇。
Obvious deformation and vibration for guideway and piers,which influence structure safety,car running,and riding comfort of passengers directly,will appear when high-speed maglev trains run on the guideway/pier system.Studies on response of both simple and continuous guideway girders in maglev system have rarely taken account in the effect of piers until now.However,the influence of piers on dynamic characteristics of the whole structure will not be ignored with their heights getting larger and have great effect on the stiffness of the system.The dynamic interaction of maglev train and guideway/pier system has become an important problem in the course of high-speed maglev transport construction.
A high-speed maglev train/guideway dynamic model considering pier vibration is established in the thesis.Based on the anlysis on the electromagnetic interaction and natural vibration of the guideway/pier system,the dynamic responses of vehicle, guideway and pier are calculated with the in-suit tested irregulaties as the outside motivation for the train-guideway-pier system.According to the simulation,the basic principle of the dynamic responses may provide theoretic foundation and refrence for parameter choice and scheme selection.The main research is as follows.
(1) Based on the analysis on the electromagnetic and mechanical coupling relationship between the high-speed maglev train,guideway and pier,a dynamic model is established by means of modal analysis.The model applies theories of structure dynamics,vehicle dynamics and electromagnetic control.A programme on trainguideway -pier dynamic analysis is written,whose calculating results are validated by in-suit tested datum.
(2) The characters of the horizontal,vertical,longitudinal section and structures on the maglev line are concluded.The technical requirements on system parameter, guideway and supporting structure are listed.The influence factors on the control parameters of riding comfort,guideway and supporting structure deformation are analyzed and compared with those of high-speed railway.The research here privides evaluating standard for dynamic performance of the guideway/pier system.
(3) A electromagnetic interaction model is established,by means of which the influence of control scheme,control paremeters,guideway parameters on suspension performance are discussed.A series of electromagnetic parameters that ensure steady suspension are gained,the principles that may suppress oversize vibration are brought out.
(4) A maglev guideway/pier system is established according to the engineering practice and calculate the eigenvalues and modes by subspace iteration method.The influence of guideway type,restraint,height and mass of pier,span numbers on natural vibration of the guideway/pier system are studied.The dynamic characteristics of the guideway/pier system provide foundation for analyzing the running safety and riding comfort when maglev trains run on the system.
(5) The dynamic responses of the train,guideway and pier are simulated by the maglev train-guideway-pier model with in-suit tested irregularities as outside motivation.The vertical and horizontal resonances of the guideway/pier system are analyzed and the dynamic performance of the single and continuous guideway are evaluated.119 figures,20 tables,138 references.
本文结合国家自然科学基金资助项目《高速磁浮交通轨道梁动力特性研究》(项目号:50578010)的研究工作,建立了考虑墩体参振的高速磁浮列车-轨道梁系统动力分析模型,在电磁相互作用和梁墩体系自振特性分析的基础上,以磁浮线路实测不平顺作为外界激励源,对高速磁浮列车运行时所引起的车辆、轨道梁、墩的各项动力响应进行了计算分析,得出了高速磁浮列车引起的梁墩体系动力响应基本规律,从而为高速磁浮梁墩参数选取和方案选择提供理论基础与参考建议。全文具体开展了如下几方面的研究工作:
(1)分析了高速磁浮列车、轨道梁、墩系统的电磁学、力学耦合关系,运用结构动力学、车辆动力学及电磁控制理论原理,采用模态综合技术,建立了考虑墩体参振的高速磁浮列车-轨道梁系统动力分析模型,给出了具体求解步骤。基于本文的分析理论以及多年的科研积累,独立编制了车-梁-墩动力分析程序。通过现场试验结果验证理论模型和分析方法的有效性。
(2)分析了磁浮线路平纵横面和线路结构主要特点,介绍了磁浮系统参数、轨道梁和下部结构相关技术要求,对乘坐舒适度控制指标、轨道梁及下部结构相关技术要求和参数选定依据和影响因素进行了综合分析,并和高速铁路相关标准进行了对比研究,为梁墩体系动力性能评价提供了评判标准。
(3)建立了电磁相互作用数学模型,研究了控制方案、控制参数、轨道梁参数对悬浮性能的影响规律,确定了保证高速磁浮列车稳定悬浮的磁轨参数匹配关系,提出了控制悬浮阶段过大振动的原则。
(4)以工程实践为背景,建立了磁浮交通轨道梁墩体系有限元模型,采用子空间迭代法计算了梁墩体系特征值和模态,分析了不同梁型、约束、墩高、墩重、跨数等因素对梁墩体系自振特性的影响,阐明了恒载作用下轨道梁墩体系动力特性,为进一步分析高速磁浮列车作用下梁墩体系动力响应及运行安全性和舒适性奠定基础。
(5)采用车-梁-墩动力相互作用模型,以磁浮线路实测不平顺作为外界激励源,对高速磁浮列车运行时所引起的车辆、轨道梁、墩的各项动力响应进行计算分析,研究了梁墩体系垂向共振和横向共振条件,对简支梁和两跨连续梁进行了动力学性能分析评估,阐明了高速磁浮列车作用下轨道梁墩体系动力特性。图119幅,表20个,参考文献138篇。
Obvious deformation and vibration for guideway and piers,which influence structure safety,car running,and riding comfort of passengers directly,will appear when high-speed maglev trains run on the guideway/pier system.Studies on response of both simple and continuous guideway girders in maglev system have rarely taken account in the effect of piers until now.However,the influence of piers on dynamic characteristics of the whole structure will not be ignored with their heights getting larger and have great effect on the stiffness of the system.The dynamic interaction of maglev train and guideway/pier system has become an important problem in the course of high-speed maglev transport construction.
A high-speed maglev train/guideway dynamic model considering pier vibration is established in the thesis.Based on the anlysis on the electromagnetic interaction and natural vibration of the guideway/pier system,the dynamic responses of vehicle, guideway and pier are calculated with the in-suit tested irregulaties as the outside motivation for the train-guideway-pier system.According to the simulation,the basic principle of the dynamic responses may provide theoretic foundation and refrence for parameter choice and scheme selection.The main research is as follows.
(1) Based on the analysis on the electromagnetic and mechanical coupling relationship between the high-speed maglev train,guideway and pier,a dynamic model is established by means of modal analysis.The model applies theories of structure dynamics,vehicle dynamics and electromagnetic control.A programme on trainguideway -pier dynamic analysis is written,whose calculating results are validated by in-suit tested datum.
(2) The characters of the horizontal,vertical,longitudinal section and structures on the maglev line are concluded.The technical requirements on system parameter, guideway and supporting structure are listed.The influence factors on the control parameters of riding comfort,guideway and supporting structure deformation are analyzed and compared with those of high-speed railway.The research here privides evaluating standard for dynamic performance of the guideway/pier system.
(3) A electromagnetic interaction model is established,by means of which the influence of control scheme,control paremeters,guideway parameters on suspension performance are discussed.A series of electromagnetic parameters that ensure steady suspension are gained,the principles that may suppress oversize vibration are brought out.
(4) A maglev guideway/pier system is established according to the engineering practice and calculate the eigenvalues and modes by subspace iteration method.The influence of guideway type,restraint,height and mass of pier,span numbers on natural vibration of the guideway/pier system are studied.The dynamic characteristics of the guideway/pier system provide foundation for analyzing the running safety and riding comfort when maglev trains run on the system.
(5) The dynamic responses of the train,guideway and pier are simulated by the maglev train-guideway-pier model with in-suit tested irregularities as outside motivation.The vertical and horizontal resonances of the guideway/pier system are analyzed and the dynamic performance of the single and continuous guideway are evaluated.119 figures,20 tables,138 references.
引文
[1]铁道科学研究院高速铁路技术研究总体组.高速铁路技术[M].北京:中国铁道出版社,2005.
[2]吴祥明.磁浮列车[M].上海:上海科技出版社,2003.
[3]刘华清.德国磁悬浮列车Transrapid[M].成都:电子科技大学出版社,1995.
[4]魏庆朝,孔永健.磁悬浮铁路系统与技术[M].北京:中国科学技术出版社,2003.
[5]孙翔.世界各国的高速铁路[M].成都:西南交通大学出版社,1992.
[6]钱仲侯.高速铁路概论(第三版)[M].北京:中国铁道出版社,2006.
[7]严陆光.高速磁悬浮列车的战略进展与我国的发展战略[J].电工电能新技术,2002,21(4):1-12.
[8]严陆光.关于我国高速磁悬浮列车发展战略的思考[J].中国工程科学,2002,4(12):40-46.
[9]吴祥明,常文森,刘万明.上海高速磁浮列车及磁浮技术发展刍议[J].综合运输,2005(1):28-31.
[10]正田英介等编.磁气浮上の铁道技术[M].东京:ォ—ム社,1992.
[11]史黎明,李耀华,徐善纲.磁悬浮方式与磁浮列车的几种方案比较[J].磁浮交通,2004,1(1):67-71.
[12]邹振民.新世纪城市理想的交通工具—介绍日本HSST磁悬浮列车系统[J].铁道通信信号,2001,37(11):37-39.
[13]Masaaki Fujino,罗芳.HSST—100的全面运行试验与名古屋东山坡线工程[J].国外铁道车辆,2001,38(2):29-31.
[14]手岛雄一,安藤直树,邹振民.2005年日本国际博览会交通通道将正式启用HSST[J].世界轨道交通,2004,1(3):23-26.
[15]李云钢,常文森,闫宇壮.美国新型结构磁悬浮交通技术分析与比较[J].机车电传动,2006(3):6-9,39.
[16]蒲黔辉,成文佳等.青城山磁浮列车工程示范线高架桥设计[J].桥梁建设,2001,1(6):28-30.
[17]国防科技大学.磁悬浮列车关键技术研究—悬浮与导向系统技术报告[R].1996.
[18]西南交通大学.都江堰青城山磁浮列车工程示范线可行性研究报告[R].1997.
[19]沈志云等.在我国建设世界上第一条高温超导磁悬浮列车试运行线的建议[J].中国科学院院刊,19(1):28.
[20]王家素,王素玉,连级三.高温超导磁浮车[J].低温与超导,1997,25(1):17-22.
[21]吴定俊.提速状态下车桥耦合振动理论与桥梁横向动力性能的研究[D].上海:同济大学,2005.
[22]凌知民.铁路高墩桥梁车桥耦合振动及横风对车桥响应的影响研究[D].上海:同济大学.2004.
[23]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996.
[24]Wills R.Appendix of the repoet of commissioners appointed to inquire application of iron to railway structures[R].His majesty's stationary office,London,1849.
[25]陈英俊.车辆荷载下桥梁振动理论的演进[J].桥梁建设,1975,2:21-36.
[26]Timonshenko S P.Forced vibration of prismatic bars[R].Izvestiya kievskogo politekhnicheskogo institute,1908.
[27]Timonshenko S P.On the forced vibration of bridges[M].Philosoph,Magzine Ser,1922,6.
[28]Inglis C.E.A mathematical treatise on vibrations in railway bridges[M].London:Cambridge,1934.
[29]沈锐利.高速铁路桥梁与车辆耦合振动研究[D].成都:西南交通大学,1998.
[30]曾庆元,郭向荣.列车桥梁时变系统振动分析理论及应用[M].北京:中国铁道出版社,1999.
[31]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2003.
[32]蔡成标.高速铁路列车—线路—桥梁耦合振动理论及应用研究[D].成都:西南交通大学,2004.
[33]李小珍.高速铁路列车—桥梁系统耦合振动理论及应用研究[D].成都:西南交通大学,2000.
[34]高芒芒.高速铁路列车—线路—桥梁耦合振动及列车走行性研究[D].北京:铁道科学研究院,2001.
[35]李小珍,强士中.列车-桥梁耦合振动研究的现状与发展趋势.铁道学报,2002,24(5):112-120.
[36]Fryba,L.Vibration of solids and structures under moving loads[M].Groningen:Noordhoff International Publishing,1972.
[37]Yang,Y.B.,Yan,J.D.and Hsu L.C..1997.Vibration of simple beams due to trains moving at high speeds[J].J.Engineering Structures.19(11):936-944.
[38]Yan,J.D.,and Yang,Y.B.2004a.A Wideband MTMD System for Reducing the Dynamic Response of Continuous Truss Bridges to Moving Train Loads[J].J.Engineering Structure.26(12):1795-1807.
[39]夏禾.车—梁—墩体系动力相互作用分析[J].土木工程学报,1992,25(2):3-11.
[40]马坤全等.列车通过抢修高墩横向振动随机分析[J].铁道学报,1998,20(1):88-94.
[41]吴定俊,李守龙.墩体设计对梁跨结构振动的影响[J].铁道学报,2002,24(6):73-77.
[42]凌知民,曹雪琴.铁路高墩连续梁桥车桥耦合振动响应分析[J].铁道学报,2002,24(5):98-102.
[43]郭薇薇,夏禾.直线电机列车作用下高架桥的动力响应分析[J].中国铁道科学,2007,28(4):55-60.
[44]Chiu.W.S,Smith.R.G,Wormley.D.N.Influence of vehicle and distributed guideway parameters on high speed vehicle-guideway dynamic interactions[J].J.of Dynamic System,Measurement and Control,Trans.ASME,1971,93:25-34.
[45]Cai.Y,Chen.S.S,Rote.D.M,et al.Vehicle/Guideway dynamic interaction in maglev system [J].Journal of Dynamic System,Measurement and Control,Trans,ASME.1996,118:526-530.
[46]M.Nagai,M.lguchi.Vibrational characteristics of electromagnetic levitation vehicles-guideway system[C].The dynamics of vehicles on roads and on railway tracks.Proc.6~(th) IAVSD-IUTAM Symposium.Berlin,1979:352-366.
[47]赵春发,翟婉明,蔡成标.磁浮车辆/高架桥垂向耦合动力学研究[J].铁道学报,2001, 23(5):27-33.
[48]曾佑文,王少华,张昆仑.EMS磁浮列车—轨道垂向耦合动力学研究[J].铁道学报,1999,21(2):22-25.
[49]Tsunashima.H,Abe.M.Static and Dynamic Performance of Permanent Magnet Suspension for Maglev Transport Vehicle[l].Vehicle System Dynamics,Vol.29,1998,pp.83-111.
[50]赵春发,翟婉明,王开云.磁浮车辆随机振动响应分析及平稳性研究[J].中国机械工程,2002,13(16).
[51]范钦海.高速常导磁悬浮车辆对轨道平顺性要求的探讨[J].中国铁道科学,2002,23(1):73-76.
[52]Nagai,M.S.N.K.G.R.,C Hen.Control of magnetic suspension to suppress the self-excited vibration of a flexible guideway[J].IEEE Transactions on industrial electronics.1986,52(478):1780-1786.
[53]周又和,武建军,郑晓静.磁浮列车的动力稳定性分析与Liapunov指数[J].力学学报,2000,32(1):42-51.
[54]武建军,郑晓静,周又和.弹性轨道上二自由度磁悬浮列车的动力特性分析[J].振动工程学报,1999,12(4):439-446.
[55]柳贵东,佘龙华.Hopf分岔的劳斯判据及磁悬浮系统的振动分析[J].振动、测试与诊断,2003,23(4):276-278.
[56]施晓红,佘龙华,常文森.EMS磁浮列车车/轨耦合系统的分岔现象研究[J].力学学报,2004,36(5):634-639.
[57]谢云德,常文森.电磁型(EMS)磁悬浮列车系统铅垂方向的建模与仿真[J].铁道学报,1999,18(4):47-54.
[58]谢云德,常文森.电磁型磁浮列车单铁力的计算及运动稳定性和可控性研究[J].铁道学报,1995,17(1):41-48
[59]李云钢.EMS型磁浮列车悬浮控制技术研究[D].国防科技大学博士论文,1997.
[60]曾佑文,王少华,张昆仑.磁浮列车车辆-轨道耦合振动及悬挂参数研究[D].西南交通大学学报,1999,34(2):168-173.
[61]谢云德.EMS型磁浮列车系统动力学建模与仿真研究[D].国防科技大学博士论文,1998.
[62]赵春发.磁浮车辆系统动力学[D].西南交通大学博士论文,2002.
[63]Kort(u|¨)m W.Review of multibody computer codes for vehicle system dynamics[J].Vehicle System Dynamics,1993,22:3-31.
[64]邓永权,罗世辉等.基于SIMPACK的磁悬浮车辆耦合动力学性能仿真模型[J].交通运输工程学报,2007,7(2):12-20.
[65]杨予,滕念管,黄醒春,滕延锋.承受移动均布质量的简支梁振动反应分析[J].振动与冲击,2005,24(3):19-22.
[66]滕延锋,滕念管,寇新建.承受移动均布二系悬挂模型的磁浮三跨连续梁振动分析[J].振动与冲击,2008,27(3):120-123.
[67]Wanming ZHAI,Chunfa ZHAO,Chengbiao CAI.Dynamic Simulation of the EMS Maglev Vehicle-Guideway-Controller Coupling System[C].MAGLEV'2005,Shanghai,China,2005.
[68]Jin Shi,Qingchao Wei,Yang Zhao.Analysis of Dynamic Response of the High-Speed EMS Maglev Vehicle/Guideway Coupling System with Random Irregularity[J].Vehicle System Dynamics,Vol.45,No.12,December 2007:1077-1095.
[69]SHI Jin,WEI Qing-chao.Study on Dynamic Characteristic of the EMS Maglev Guideway [C].Proceedings of the 2nd International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,September 20-22,2005,ISEV.
[70]时瑾,魏庆朝.随机不平顺激励下磁浮车辆轨道梁动力响应[J].力学学报,2006,38(6):850-857.
[71]时瑾.高速常导磁浮车辆—线路动力响应研究[D].北京:北京交通大学,2006.
[72]时瑾,魏庆朝.高速磁浮交通平竖曲线主要技术参数研究[J].全国交通运输学科博士生学术论坛论文集,2005.
[73]Project Guidelines,Transrapid Shanghai Project Document,Basis for Dimensioning of Guideways[S],Doc.No.11170,14.12.2000
[74]System Specification,Transrapid Shanghai Project Document,Transrapid[S],Doc.No.11252,14.12.2000.
[75]Requirement Specification,Transrapid Shanghai Project Document,Guideway[S],Doc.No.1115714.12.2000.
[76]Project Guidelines,Transrapid Shanghai Project Document,Basis for Realization of Guideway Geometry[S],Doc.No.11157,14.12.2000.
[77]王悦明,王新锐.客车舒适度的评定[J].铁道机车车辆,2000,(3):1-4.
[78]GB5599-85,铁道车辆动力学性能评定和试验鉴定规范[S].
[79]TB/T2369-1993,铁道机车动力学性能试验鉴定方法及评定标准[S].
[80]铁建设[2007]47号,新建时速300～350公里客运专线铁路设计暂行规定(上、下)[S].2007.
[81]余华.基于非线性电磁力的EMS高速磁浮车桥耦合振动研究[D].上海:同济大学,2009.
[82]L.E.Daniels,D.R.Ahlbeck,Z.J.Stekly,G.M.Gregorick,Influence of Guideway Flexibility on Maglev Vehicle/Guideway Dynamic Forces,(Maglev Structural Dynamics)[R].National Maglev Initiative,Federal Railroad Administration,DOT/FRA/NMI-92/09,July 1992
[83]J.D.Yan.Vibration control of maglev vehicles traveling over a flexible guideway[J].Journal of sound and vibration,321(2009):184-200.
[84]贾素红.高速磁浮轨道梁合理型式研究[D].成都:西南交通大学学位论文,2005.
[85]翟婉明.车辆-轨道耦合动力学(第三版)[M].北京:科学出版社,2007.
[86]张定贤.机车车辆轨道系统动力学[M].北京:中国铁道出版社,1996.
[87]王福天.车辆系统动力学[M].北京:中国铁道出版社,1994.
[88]詹斐生.机车动力学[M].北京:中国铁道出版社,1990.
[89]费学博.高等动力学[M].浙江大学出版社,1991.
[90]P.K.Sinha.Electromagnetic Suspension Dynamics&control[M].Peter Peregrinus Ltd,1987.
[91]郑树彬,林建辉,林国斌.用于轨检信号提取的线性相位IIR移变滤波器[J].西南交通大学学报,2007:42(2):211-216.
[92]杜鹤亭.长波长轨道不平顺检测中的数字滤波器方法[J].中国铁道科学,2000,21(4):58-65.
[93]李莉,孟光.磁浮车不能稳定悬停在钢轨道框架上的原因分析[J].城市轨道交通研究,2006,9(5):40-42.
[94]王明明.车辆荷载作用下高墩大跨连续刚构桥的动力反应分析[D].长沙:湖南大学,2006.
[95]K.J.Bathe,E.L.Wilson.Large Eigenvalue Problems in Dynamic Analysis[J].Journal of Engineering Mechanics Division,ASCE,1972,98(8):1471-1485.
[96]E.L.Wilson,T.Itoh.An Eigensolution Strategy for Large Systems[J].Computer &Structures,1983,16(1-4):259-265.
[97]夏禾,郭薇薇,张楠.车桥系统共振机理和共振条件分析[J].铁道学报,2006,28(5):52-58.
[98]W.W.Guo,H.Xia.Resonance Analysis of Train-bridge Dynamic Interaction System[C].Proceedings of the 2~(nd) International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,September 20-22,2005,ISEV.
[99]Yang Yeong-Bin,Yau Jong-Dar,Hsu Lin-Ching.Vibration of simple beams due to trains moving at high speeds[J].Engineering Structures,1997,19(11):936-944.
[100]Yingjie Wang,QingChao Wei,Jin Shi,Xuyou Long.Dynamic response of two-span continuous beam under moving loads[C].Proceedings of the 4~(th) International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,October 28-30,2009,ISEV.
[101]Yan,J.D.2004b.Suppression of train-induced vibrations of continuous truss bridges by hybrid TMDs[C].ICTAM2004,15-21.
[102]Jong-Dar Yau.Resonance of continuous bridges due to high speed trains[J].Journal of marine science and technology,vol.9,No.1,2001,pp.14-20.
[103]Seetapan,P.and Chucheepsakul,S..2006.Dynamic responses of a two-span beam subjected to high speed 2DOF sprung vehicles[J].J.Structural Stability and Dynamics.6(3):413-430.
[104]宣言,王澜.客运专线曲线线路车线耦合系统动力学性能与无砟轨道结构振动响应的仿真研究[J].中国铁道科学,2007,28(5):136-138.
[105]梁红燕.高速磁悬浮铁路线路平纵断面设计标准的研究[D].成都:西南交通大学,2003.
[106]刘宏友.高速列车中的关键动力学问题研究[D].成都:西南交通大学,2003.
[107]龙许友.高速铁路线路参数对车线动力响应影响分析及参数优化与匹配研究[D].北京:北京交通大学.2008.
[108]Zhai W.M.,Sun X.A detailed model for investigating vertical interaction between railwayvehicle and track[J].Vehicle Systems Dynamics,1994,23(suppl.):603-615.
[109]Delgado R.Moreno,C.S.M.dos Santos R.modelling of railway bridge-vehicle interaction on high speed tracks[J].Computers & Structures,1997,63(3):511-523.
[110]Tanabe,M.,Wakui,H.,Matsumoto,N.,Okuda,H.,Sogabe,M.,Komiya,S.Computational model of a Shinkansen train running on the railway structure and the industrial applications[J].Journal of Materials Processing Technology,2003,140(1-3):705-710.
[111]Sun Y.Q.,Dhanasekar M.A dynamic model for the vertical interaction of the rail track and wagon system[J].International Journal of Solids and Structures,2002,39(5):1337-1359.
[112]K.Hou J.Kalousek,Dong R.A dynamic model for an asymmetrical vehicle/track system[J]. Journal of Materials Processing Technology,2003,267(3):591-604.
[113]Nielsen J.C.O.,Oscarsson J.Simulation of dynamic train track interaction with state-dependent track properties[J].Journal of Materials Processing Technology,2004,275(3-5):515-532.
[114]Xia He,Zhang Nan.Dynamic analysis of railway bridge under high-speed trains[J].Computers & Structures,2005,83(23-24):1891-1901.
[115]杨中平.日本高速铁路技术[M].北京:中国铁道出版社,2006.
[116]刘万明.我国高速铁路客运专线主要技术经济问题研究[D].成都:西南交通大学,2002.
[117]单德山.高速铁路曲线梁桥车桥耦合振动分析及大跨度曲线梁桥设计研究[D].成都:西南交通大学,1999.
[118]张格明.中高速条件下车线桥动力分析模型与轨道不平顺影响[D].北京:铁道科学研究院.2001.
[119]俞展猷.高速列车舒适度的评价[J].铁道机车车辆,1999,(2):1-5.
[120]米隆,招阳,魏庆朝.磁浮交通系统线路缓和曲线参数取值方法研究[J].北京交通大学学报(自然科学版),2007,31(4):92-95,100.
[121]招阳,魏庆朝.高速磁浮线路圆曲线参数取值研究[J].北京交通大学学报(自然科学版),2007,31(4):101-105.
[122]刘万明.高速磁悬浮线路规划设计理论研究[J].学术动态(成都),2003,3(3):26-28.
[123]陈泽深,王成国.铁道车辆动力学与控制[M].北京:中国铁道出版社,2004.
[124]V.K.Garg,R.V.Dukkipati著,沈利人译.铁道车辆系统动力学[M].成都:西南交通大学出版社,1998.
[125]王其昌.高速铁路土木工程[M].成都:西南交通大学出版社,1999.
[126]李远富.线路勘测设计[M].北京:高等教育出版社,2004.
[127]范俊杰.现代铁路轨道[M].北京:中国铁道出版社,2004.
[128]卢祖文.客运专线铁路轨道[M].北京:中国铁道出版社,2005.
[129]严隽耄.车辆工程[M].北京:中国铁道出版社,1992.
[130]陈果.车辆—轨道耦合系统随机振动分析[D].成都:西南交通大学,2000.
[131]张楠.高速铁路铰接式列车车桥动力耦合问题的理论分析与实验研究[D].北京:北京交通大学,2002.
[132]佐藤吉彦著,徐涌等译.新轨道力学[M].北京:中国铁道出版社,2001.
[133]Clough,Penzien著,王光远译.结构动力学[M].北京:科学出版社,1988.
[134]邓永权.磁悬浮列车静悬稳定性与仿真分析[D].成都:西南交通大学,2005.
[135]商海波.磁悬浮数字控制方法及其实现[D].成都:西南交通大学,2003.
[136]吴建军.DSP磁浮列车悬浮控制器的研究[D].成都:西南交通大学,2001.
[137]杨予.磁悬浮轨道梁在车辆荷载作用下的竖向振动特性研究[D].成都:西南交通大学,2005.
[138]V.I.Gulyaev,M.Nabil.Resonant Interaction of a Beam and an Elastic Foundation During the Motion of a Periodic System of Concentrated Loads[J].International Applied Mechanics.2005,41(5):560-565
[2]吴祥明.磁浮列车[M].上海:上海科技出版社,2003.
[3]刘华清.德国磁悬浮列车Transrapid[M].成都:电子科技大学出版社,1995.
[4]魏庆朝,孔永健.磁悬浮铁路系统与技术[M].北京:中国科学技术出版社,2003.
[5]孙翔.世界各国的高速铁路[M].成都:西南交通大学出版社,1992.
[6]钱仲侯.高速铁路概论(第三版)[M].北京:中国铁道出版社,2006.
[7]严陆光.高速磁悬浮列车的战略进展与我国的发展战略[J].电工电能新技术,2002,21(4):1-12.
[8]严陆光.关于我国高速磁悬浮列车发展战略的思考[J].中国工程科学,2002,4(12):40-46.
[9]吴祥明,常文森,刘万明.上海高速磁浮列车及磁浮技术发展刍议[J].综合运输,2005(1):28-31.
[10]正田英介等编.磁气浮上の铁道技术[M].东京:ォ—ム社,1992.
[11]史黎明,李耀华,徐善纲.磁悬浮方式与磁浮列车的几种方案比较[J].磁浮交通,2004,1(1):67-71.
[12]邹振民.新世纪城市理想的交通工具—介绍日本HSST磁悬浮列车系统[J].铁道通信信号,2001,37(11):37-39.
[13]Masaaki Fujino,罗芳.HSST—100的全面运行试验与名古屋东山坡线工程[J].国外铁道车辆,2001,38(2):29-31.
[14]手岛雄一,安藤直树,邹振民.2005年日本国际博览会交通通道将正式启用HSST[J].世界轨道交通,2004,1(3):23-26.
[15]李云钢,常文森,闫宇壮.美国新型结构磁悬浮交通技术分析与比较[J].机车电传动,2006(3):6-9,39.
[16]蒲黔辉,成文佳等.青城山磁浮列车工程示范线高架桥设计[J].桥梁建设,2001,1(6):28-30.
[17]国防科技大学.磁悬浮列车关键技术研究—悬浮与导向系统技术报告[R].1996.
[18]西南交通大学.都江堰青城山磁浮列车工程示范线可行性研究报告[R].1997.
[19]沈志云等.在我国建设世界上第一条高温超导磁悬浮列车试运行线的建议[J].中国科学院院刊,19(1):28.
[20]王家素,王素玉,连级三.高温超导磁浮车[J].低温与超导,1997,25(1):17-22.
[21]吴定俊.提速状态下车桥耦合振动理论与桥梁横向动力性能的研究[D].上海:同济大学,2005.
[22]凌知民.铁路高墩桥梁车桥耦合振动及横风对车桥响应的影响研究[D].上海:同济大学.2004.
[23]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996.
[24]Wills R.Appendix of the repoet of commissioners appointed to inquire application of iron to railway structures[R].His majesty's stationary office,London,1849.
[25]陈英俊.车辆荷载下桥梁振动理论的演进[J].桥梁建设,1975,2:21-36.
[26]Timonshenko S P.Forced vibration of prismatic bars[R].Izvestiya kievskogo politekhnicheskogo institute,1908.
[27]Timonshenko S P.On the forced vibration of bridges[M].Philosoph,Magzine Ser,1922,6.
[28]Inglis C.E.A mathematical treatise on vibrations in railway bridges[M].London:Cambridge,1934.
[29]沈锐利.高速铁路桥梁与车辆耦合振动研究[D].成都:西南交通大学,1998.
[30]曾庆元,郭向荣.列车桥梁时变系统振动分析理论及应用[M].北京:中国铁道出版社,1999.
[31]夏禾.车辆与结构动力相互作用[M].北京:科学出版社,2003.
[32]蔡成标.高速铁路列车—线路—桥梁耦合振动理论及应用研究[D].成都:西南交通大学,2004.
[33]李小珍.高速铁路列车—桥梁系统耦合振动理论及应用研究[D].成都:西南交通大学,2000.
[34]高芒芒.高速铁路列车—线路—桥梁耦合振动及列车走行性研究[D].北京:铁道科学研究院,2001.
[35]李小珍,强士中.列车-桥梁耦合振动研究的现状与发展趋势.铁道学报,2002,24(5):112-120.
[36]Fryba,L.Vibration of solids and structures under moving loads[M].Groningen:Noordhoff International Publishing,1972.
[37]Yang,Y.B.,Yan,J.D.and Hsu L.C..1997.Vibration of simple beams due to trains moving at high speeds[J].J.Engineering Structures.19(11):936-944.
[38]Yan,J.D.,and Yang,Y.B.2004a.A Wideband MTMD System for Reducing the Dynamic Response of Continuous Truss Bridges to Moving Train Loads[J].J.Engineering Structure.26(12):1795-1807.
[39]夏禾.车—梁—墩体系动力相互作用分析[J].土木工程学报,1992,25(2):3-11.
[40]马坤全等.列车通过抢修高墩横向振动随机分析[J].铁道学报,1998,20(1):88-94.
[41]吴定俊,李守龙.墩体设计对梁跨结构振动的影响[J].铁道学报,2002,24(6):73-77.
[42]凌知民,曹雪琴.铁路高墩连续梁桥车桥耦合振动响应分析[J].铁道学报,2002,24(5):98-102.
[43]郭薇薇,夏禾.直线电机列车作用下高架桥的动力响应分析[J].中国铁道科学,2007,28(4):55-60.
[44]Chiu.W.S,Smith.R.G,Wormley.D.N.Influence of vehicle and distributed guideway parameters on high speed vehicle-guideway dynamic interactions[J].J.of Dynamic System,Measurement and Control,Trans.ASME,1971,93:25-34.
[45]Cai.Y,Chen.S.S,Rote.D.M,et al.Vehicle/Guideway dynamic interaction in maglev system [J].Journal of Dynamic System,Measurement and Control,Trans,ASME.1996,118:526-530.
[46]M.Nagai,M.lguchi.Vibrational characteristics of electromagnetic levitation vehicles-guideway system[C].The dynamics of vehicles on roads and on railway tracks.Proc.6~(th) IAVSD-IUTAM Symposium.Berlin,1979:352-366.
[47]赵春发,翟婉明,蔡成标.磁浮车辆/高架桥垂向耦合动力学研究[J].铁道学报,2001, 23(5):27-33.
[48]曾佑文,王少华,张昆仑.EMS磁浮列车—轨道垂向耦合动力学研究[J].铁道学报,1999,21(2):22-25.
[49]Tsunashima.H,Abe.M.Static and Dynamic Performance of Permanent Magnet Suspension for Maglev Transport Vehicle[l].Vehicle System Dynamics,Vol.29,1998,pp.83-111.
[50]赵春发,翟婉明,王开云.磁浮车辆随机振动响应分析及平稳性研究[J].中国机械工程,2002,13(16).
[51]范钦海.高速常导磁悬浮车辆对轨道平顺性要求的探讨[J].中国铁道科学,2002,23(1):73-76.
[52]Nagai,M.S.N.K.G.R.,C Hen.Control of magnetic suspension to suppress the self-excited vibration of a flexible guideway[J].IEEE Transactions on industrial electronics.1986,52(478):1780-1786.
[53]周又和,武建军,郑晓静.磁浮列车的动力稳定性分析与Liapunov指数[J].力学学报,2000,32(1):42-51.
[54]武建军,郑晓静,周又和.弹性轨道上二自由度磁悬浮列车的动力特性分析[J].振动工程学报,1999,12(4):439-446.
[55]柳贵东,佘龙华.Hopf分岔的劳斯判据及磁悬浮系统的振动分析[J].振动、测试与诊断,2003,23(4):276-278.
[56]施晓红,佘龙华,常文森.EMS磁浮列车车/轨耦合系统的分岔现象研究[J].力学学报,2004,36(5):634-639.
[57]谢云德,常文森.电磁型(EMS)磁悬浮列车系统铅垂方向的建模与仿真[J].铁道学报,1999,18(4):47-54.
[58]谢云德,常文森.电磁型磁浮列车单铁力的计算及运动稳定性和可控性研究[J].铁道学报,1995,17(1):41-48
[59]李云钢.EMS型磁浮列车悬浮控制技术研究[D].国防科技大学博士论文,1997.
[60]曾佑文,王少华,张昆仑.磁浮列车车辆-轨道耦合振动及悬挂参数研究[D].西南交通大学学报,1999,34(2):168-173.
[61]谢云德.EMS型磁浮列车系统动力学建模与仿真研究[D].国防科技大学博士论文,1998.
[62]赵春发.磁浮车辆系统动力学[D].西南交通大学博士论文,2002.
[63]Kort(u|¨)m W.Review of multibody computer codes for vehicle system dynamics[J].Vehicle System Dynamics,1993,22:3-31.
[64]邓永权,罗世辉等.基于SIMPACK的磁悬浮车辆耦合动力学性能仿真模型[J].交通运输工程学报,2007,7(2):12-20.
[65]杨予,滕念管,黄醒春,滕延锋.承受移动均布质量的简支梁振动反应分析[J].振动与冲击,2005,24(3):19-22.
[66]滕延锋,滕念管,寇新建.承受移动均布二系悬挂模型的磁浮三跨连续梁振动分析[J].振动与冲击,2008,27(3):120-123.
[67]Wanming ZHAI,Chunfa ZHAO,Chengbiao CAI.Dynamic Simulation of the EMS Maglev Vehicle-Guideway-Controller Coupling System[C].MAGLEV'2005,Shanghai,China,2005.
[68]Jin Shi,Qingchao Wei,Yang Zhao.Analysis of Dynamic Response of the High-Speed EMS Maglev Vehicle/Guideway Coupling System with Random Irregularity[J].Vehicle System Dynamics,Vol.45,No.12,December 2007:1077-1095.
[69]SHI Jin,WEI Qing-chao.Study on Dynamic Characteristic of the EMS Maglev Guideway [C].Proceedings of the 2nd International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,September 20-22,2005,ISEV.
[70]时瑾,魏庆朝.随机不平顺激励下磁浮车辆轨道梁动力响应[J].力学学报,2006,38(6):850-857.
[71]时瑾.高速常导磁浮车辆—线路动力响应研究[D].北京:北京交通大学,2006.
[72]时瑾,魏庆朝.高速磁浮交通平竖曲线主要技术参数研究[J].全国交通运输学科博士生学术论坛论文集,2005.
[73]Project Guidelines,Transrapid Shanghai Project Document,Basis for Dimensioning of Guideways[S],Doc.No.11170,14.12.2000
[74]System Specification,Transrapid Shanghai Project Document,Transrapid[S],Doc.No.11252,14.12.2000.
[75]Requirement Specification,Transrapid Shanghai Project Document,Guideway[S],Doc.No.1115714.12.2000.
[76]Project Guidelines,Transrapid Shanghai Project Document,Basis for Realization of Guideway Geometry[S],Doc.No.11157,14.12.2000.
[77]王悦明,王新锐.客车舒适度的评定[J].铁道机车车辆,2000,(3):1-4.
[78]GB5599-85,铁道车辆动力学性能评定和试验鉴定规范[S].
[79]TB/T2369-1993,铁道机车动力学性能试验鉴定方法及评定标准[S].
[80]铁建设[2007]47号,新建时速300～350公里客运专线铁路设计暂行规定(上、下)[S].2007.
[81]余华.基于非线性电磁力的EMS高速磁浮车桥耦合振动研究[D].上海:同济大学,2009.
[82]L.E.Daniels,D.R.Ahlbeck,Z.J.Stekly,G.M.Gregorick,Influence of Guideway Flexibility on Maglev Vehicle/Guideway Dynamic Forces,(Maglev Structural Dynamics)[R].National Maglev Initiative,Federal Railroad Administration,DOT/FRA/NMI-92/09,July 1992
[83]J.D.Yan.Vibration control of maglev vehicles traveling over a flexible guideway[J].Journal of sound and vibration,321(2009):184-200.
[84]贾素红.高速磁浮轨道梁合理型式研究[D].成都:西南交通大学学位论文,2005.
[85]翟婉明.车辆-轨道耦合动力学(第三版)[M].北京:科学出版社,2007.
[86]张定贤.机车车辆轨道系统动力学[M].北京:中国铁道出版社,1996.
[87]王福天.车辆系统动力学[M].北京:中国铁道出版社,1994.
[88]詹斐生.机车动力学[M].北京:中国铁道出版社,1990.
[89]费学博.高等动力学[M].浙江大学出版社,1991.
[90]P.K.Sinha.Electromagnetic Suspension Dynamics&control[M].Peter Peregrinus Ltd,1987.
[91]郑树彬,林建辉,林国斌.用于轨检信号提取的线性相位IIR移变滤波器[J].西南交通大学学报,2007:42(2):211-216.
[92]杜鹤亭.长波长轨道不平顺检测中的数字滤波器方法[J].中国铁道科学,2000,21(4):58-65.
[93]李莉,孟光.磁浮车不能稳定悬停在钢轨道框架上的原因分析[J].城市轨道交通研究,2006,9(5):40-42.
[94]王明明.车辆荷载作用下高墩大跨连续刚构桥的动力反应分析[D].长沙:湖南大学,2006.
[95]K.J.Bathe,E.L.Wilson.Large Eigenvalue Problems in Dynamic Analysis[J].Journal of Engineering Mechanics Division,ASCE,1972,98(8):1471-1485.
[96]E.L.Wilson,T.Itoh.An Eigensolution Strategy for Large Systems[J].Computer &Structures,1983,16(1-4):259-265.
[97]夏禾,郭薇薇,张楠.车桥系统共振机理和共振条件分析[J].铁道学报,2006,28(5):52-58.
[98]W.W.Guo,H.Xia.Resonance Analysis of Train-bridge Dynamic Interaction System[C].Proceedings of the 2~(nd) International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,September 20-22,2005,ISEV.
[99]Yang Yeong-Bin,Yau Jong-Dar,Hsu Lin-Ching.Vibration of simple beams due to trains moving at high speeds[J].Engineering Structures,1997,19(11):936-944.
[100]Yingjie Wang,QingChao Wei,Jin Shi,Xuyou Long.Dynamic response of two-span continuous beam under moving loads[C].Proceedings of the 4~(th) International Symposium on Environmental Vibrations-Prediction,Monitoring,Mitigation and Evaluation.Okayama,Japan,October 28-30,2009,ISEV.
[101]Yan,J.D.2004b.Suppression of train-induced vibrations of continuous truss bridges by hybrid TMDs[C].ICTAM2004,15-21.
[102]Jong-Dar Yau.Resonance of continuous bridges due to high speed trains[J].Journal of marine science and technology,vol.9,No.1,2001,pp.14-20.
[103]Seetapan,P.and Chucheepsakul,S..2006.Dynamic responses of a two-span beam subjected to high speed 2DOF sprung vehicles[J].J.Structural Stability and Dynamics.6(3):413-430.
[104]宣言,王澜.客运专线曲线线路车线耦合系统动力学性能与无砟轨道结构振动响应的仿真研究[J].中国铁道科学,2007,28(5):136-138.
[105]梁红燕.高速磁悬浮铁路线路平纵断面设计标准的研究[D].成都:西南交通大学,2003.
[106]刘宏友.高速列车中的关键动力学问题研究[D].成都:西南交通大学,2003.
[107]龙许友.高速铁路线路参数对车线动力响应影响分析及参数优化与匹配研究[D].北京:北京交通大学.2008.
[108]Zhai W.M.,Sun X.A detailed model for investigating vertical interaction between railwayvehicle and track[J].Vehicle Systems Dynamics,1994,23(suppl.):603-615.
[109]Delgado R.Moreno,C.S.M.dos Santos R.modelling of railway bridge-vehicle interaction on high speed tracks[J].Computers & Structures,1997,63(3):511-523.
[110]Tanabe,M.,Wakui,H.,Matsumoto,N.,Okuda,H.,Sogabe,M.,Komiya,S.Computational model of a Shinkansen train running on the railway structure and the industrial applications[J].Journal of Materials Processing Technology,2003,140(1-3):705-710.
[111]Sun Y.Q.,Dhanasekar M.A dynamic model for the vertical interaction of the rail track and wagon system[J].International Journal of Solids and Structures,2002,39(5):1337-1359.
[112]K.Hou J.Kalousek,Dong R.A dynamic model for an asymmetrical vehicle/track system[J]. Journal of Materials Processing Technology,2003,267(3):591-604.
[113]Nielsen J.C.O.,Oscarsson J.Simulation of dynamic train track interaction with state-dependent track properties[J].Journal of Materials Processing Technology,2004,275(3-5):515-532.
[114]Xia He,Zhang Nan.Dynamic analysis of railway bridge under high-speed trains[J].Computers & Structures,2005,83(23-24):1891-1901.
[115]杨中平.日本高速铁路技术[M].北京:中国铁道出版社,2006.
[116]刘万明.我国高速铁路客运专线主要技术经济问题研究[D].成都:西南交通大学,2002.
[117]单德山.高速铁路曲线梁桥车桥耦合振动分析及大跨度曲线梁桥设计研究[D].成都:西南交通大学,1999.
[118]张格明.中高速条件下车线桥动力分析模型与轨道不平顺影响[D].北京:铁道科学研究院.2001.
[119]俞展猷.高速列车舒适度的评价[J].铁道机车车辆,1999,(2):1-5.
[120]米隆,招阳,魏庆朝.磁浮交通系统线路缓和曲线参数取值方法研究[J].北京交通大学学报(自然科学版),2007,31(4):92-95,100.
[121]招阳,魏庆朝.高速磁浮线路圆曲线参数取值研究[J].北京交通大学学报(自然科学版),2007,31(4):101-105.
[122]刘万明.高速磁悬浮线路规划设计理论研究[J].学术动态(成都),2003,3(3):26-28.
[123]陈泽深,王成国.铁道车辆动力学与控制[M].北京:中国铁道出版社,2004.
[124]V.K.Garg,R.V.Dukkipati著,沈利人译.铁道车辆系统动力学[M].成都:西南交通大学出版社,1998.
[125]王其昌.高速铁路土木工程[M].成都:西南交通大学出版社,1999.
[126]李远富.线路勘测设计[M].北京:高等教育出版社,2004.
[127]范俊杰.现代铁路轨道[M].北京:中国铁道出版社,2004.
[128]卢祖文.客运专线铁路轨道[M].北京:中国铁道出版社,2005.
[129]严隽耄.车辆工程[M].北京:中国铁道出版社,1992.
[130]陈果.车辆—轨道耦合系统随机振动分析[D].成都:西南交通大学,2000.
[131]张楠.高速铁路铰接式列车车桥动力耦合问题的理论分析与实验研究[D].北京:北京交通大学,2002.
[132]佐藤吉彦著,徐涌等译.新轨道力学[M].北京:中国铁道出版社,2001.
[133]Clough,Penzien著,王光远译.结构动力学[M].北京:科学出版社,1988.
[134]邓永权.磁悬浮列车静悬稳定性与仿真分析[D].成都:西南交通大学,2005.
[135]商海波.磁悬浮数字控制方法及其实现[D].成都:西南交通大学,2003.
[136]吴建军.DSP磁浮列车悬浮控制器的研究[D].成都:西南交通大学,2001.
[137]杨予.磁悬浮轨道梁在车辆荷载作用下的竖向振动特性研究[D].成都:西南交通大学,2005.
[138]V.I.Gulyaev,M.Nabil.Resonant Interaction of a Beam and an Elastic Foundation During the Motion of a Periodic System of Concentrated Loads[J].International Applied Mechanics.2005,41(5):560-565