基于模态叠加法和直接刚度法的列车-轨道-桥梁耦合系统高效动力分析混合算法
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摘要
为提高列车-轨道-桥梁耦合系统(Train-Track-BridgeCoupledSystem,TTBS)动力分析的计算效率,该文基于作者之前提出的TTBS动力分析混合模型,结合模态叠加法和直接刚度法,提出了一种改进的混合方法(Improved Hybrid Method,IHM)。该方法中,列车动力方程通过多刚体动力学方法建立;轨道结构动力方程通过直接刚度法建立以准确求解其高频局部振动响应,桥梁结构动力方程通过模态叠加法建立以降低其自由度数目。列车和轨道结构通过轮轨线性Hertzian接触关系耦合为列车-轨道耦合时变子系统,轨道与桥梁间通过轨-桥相互作用力的平衡迭代实现耦合。首先以朔黄重载铁路32 m简支梁桥现场试验数据验证了该文方法的正确性。然后,以CRH2型高速动车组通过万宁系杆拱桥为例,探究了桥梁振型数量对动力响应指标计算精度的影响规律,最后,对比三种不同的列车-轨道-桥梁耦合系统动力分析方法的计算结果及耗时,结果表明:同样的计算精度下,该文方法具有更高的计算效率。
To improve the computational efficiency for analyzing the vibration of train-track-bridge coupled systems(TTBSs), an improved hybrid method(IHM) is proposed by combining the direct stiffness method(DSM) and the modal superposition method(MSM) based on the hybrid method. The vibration equations of the train are established by applying multi-body dynamics. The vibration equations of the track are established by using the DSM, which can effectively display the local dynamic behavior with high frequency. The vibration equations of the bridge are established by using the MSM, a method that can efficiently reduce the degrees of freedom. The train and track are coupled as a train-track subsystem through the linear wheel-rail Hertz contact model. The train-track subsystem and the bridge subsystem are coupled by enforcing the compatibility of forces at the contact points between the track and the bridge. The proposed method is validated by the field measurement data collected from a 32 m simply supported girder bridge on the Shuo-Huang heavy-haul railway line. A numerical example of a CRH2 high speed train passing the Wan-Ning Bridge is provided to investigate the effects of the number of bridge modes on the accuracy of the dynamic responses. The computation time of the three different methods for analyzing the vibration of the TTBS is compared and the results show that the IHM has the most computational efficiency than the other two methods.
To improve the computational efficiency for analyzing the vibration of train-track-bridge coupled systems(TTBSs), an improved hybrid method(IHM) is proposed by combining the direct stiffness method(DSM) and the modal superposition method(MSM) based on the hybrid method. The vibration equations of the train are established by applying multi-body dynamics. The vibration equations of the track are established by using the DSM, which can effectively display the local dynamic behavior with high frequency. The vibration equations of the bridge are established by using the MSM, a method that can efficiently reduce the degrees of freedom. The train and track are coupled as a train-track subsystem through the linear wheel-rail Hertz contact model. The train-track subsystem and the bridge subsystem are coupled by enforcing the compatibility of forces at the contact points between the track and the bridge. The proposed method is validated by the field measurement data collected from a 32 m simply supported girder bridge on the Shuo-Huang heavy-haul railway line. A numerical example of a CRH2 high speed train passing the Wan-Ning Bridge is provided to investigate the effects of the number of bridge modes on the accuracy of the dynamic responses. The computation time of the three different methods for analyzing the vibration of the TTBS is compared and the results show that the IHM has the most computational efficiency than the other two methods.
引文
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[21]张攀,周昌盛,王平.轨下垫板刚度的时变特性及其影响研究[J].铁道标准设计,2015,59(9):49―52.Zhang Pan,Zhou Changsheng,Wang Ping.Study on Time Variant Characteristics and Effects of Rail Pad Stiffness[J].Railway Standard Design,2015,59(9):49―52.(in Chinese)
[22]Fryba L.Vibration of solids and structures under moving loads[M].Groningen,The Netherlands:Noordhoff International,1972.
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[25]Clark R A.An investigation into the dynamic effects of railway vehicle running on corrugated rail[J].Journal of Mechanical Engineering Science,1982,24(2):65―76.
[26]Ling L,Han J,Xiao X,et al.Dynamic behavior of an embedded rail track coupled with a tram vehicle[J].Journal of Vibration&Control,2015,23(14):2355―2372.
[27]Zhang N,Xia H,Guo W W,et al.A vehicle-bridge linear interaction model and its validation[J].International Journal of Structural Stability&Dynamics,2010,10(2):335―361.
[28]Li Y L,Yang S,Xia F L,et al.Vertical dynamic response of the ballastless track on long-span plate-truss cable-stayed bridges[J].Science China Technological Sciences,2015,58(2):236―247.
[29]Liu K,Reynders E,Roeck G D,et al.Experimental and numerical analysis of a composite bridge for high-speed trains[J].Journal of Sound&Vibration,2009,320(1/2):201―220.
[30]Zhu Z,Wang L,Yu Z,et al.Non-stationary random vibration analysis of railway bridges under moving heavy-haul trains[J].International Journal of Structural Stability&Dynamics,2018,(5):1850035.
[31]刘玮,曲村.高速铁路桥上有砟轨道轨枕选型方案研究[J].高速铁路技术,2011,2(3):38―42.Liu Wei,Qu Cun.Study on selection of sleepers for ballasted track on bridges of high-speed railway[J].High Speed Railway Technology,2011,2(3):38―42.(in Chinese)
[32]李星新,田启贤,郑平伟,等.大跨度高速铁路桥梁测试与分析中的技术问题[J].桥梁建设,2009(增刊2):89―92.Li Xingxin,Tian Qixian,Zheng Weiping,et al.Technical issues in testing and analysis of long span high-speed railway bridges[J].Bridge Construction,2009(Suppl 2):89―92.(in Chinese)
[2]Li H,Xia H,Soliman M,et al.Bridge stress calculation based on the dynamic response of coupled train-bridge system[J].Engineering Structures,2015,99(5):334―345.
[3]朱志辉,杨乐,王力东,等.地震作用下铁路斜拉桥动力响应及行车安全性研究[J].工程力学,2017,34(4):78―87.Zhu Zhihui,Yang Le,Wang Lidong,et al.Dynamic responses and train running safety of railway cablestayed bridge earthquakes[J].Engineering Mechanics,2017,34(4):78―87.(in Chinese)
[4]Zhai W,Xia H,Cai C,et al.High-speed train-trackbridge dynamic interactions-Part I:theoretical model and numerical simulation[J].International Journal of Rail Transportation,2013,1(1/2):3―24.
[5]李奇,程石利,励吾千,等.车轨桥中高频耦合振动分析的功率流方法及模型[J].工程力学,2016,33(12):112―118.Li Qi,Cheng Shili,Li Wuqian,et al.A power flow method and its modeling for coupling vibration analysis of train-track-bridge system in the medium-to-high frequency range[J].Engineering Mechanics,2016,33(12):112―118.(in Chinese)
[6]Dimitrakopoulos E G,Zeng Q.A three-dimensional dynamic analysis scheme for the interaction between trains and curved railway bridges[J].Computers&Structures,2015,149(2015):43―60.
[7]Kargarnovin M H,Younesian D,Thompson D,et al.Ride comfort of high-speed trains travelling over railway bridges[J].Vehicle System Dynamics,2006,43(3):173―197.
[8]Yang S C,Hwang S H.Train-track-bridge interaction by coupling direct stiffness method and mode superposition method[J].Journal of Bridge Engineering,2016,21(10):04016058.
[9]Olmos J M,Astiz M A.Analysis of the lateral dynamic response of high pier viaducts under high-speed train travel[J].Engineering Structures,2013,56(6):1384―1401.
[10]朱志辉,龚威,王力东,等.列车-轨道-桥梁耦合系统动力方程求解方法对计算精度和效率的影响[J].中国铁道科学,2016,37(5):17―26.Zhu Zhihui,Gong Wei,Wang Lidong,et al.Influence of solution method for dynamics equation of train-track-bridge coupled system on calculation precision and efficiency[J].China Railway Science,2016,37(5):17―26.(in Chinese)
[11]王少钦,马骎,夏禾,等.风-列车-大跨度悬索桥系统非线性耦合振动分析[J].工程力学,2016,33(12):150―157.Wang Shaoqing,Ma Qing,Xia He,et al.Nonlinear dynamic analysis of a wind-train-long-span suspension bridge coupling system[J].Engineering Mechanics,2016,33(12):150―157.(in Chinese)
[12]朱志辉,王小飞,吕连兵,等.卸索期间列车-斜拉桥耦合动力响应分析[J].中国铁道科学,2015,36(5):19―27.Zhu Zhihui,Wang Xiaofei,LüLianbin,et al.Coupling dynamic response of train and cable-stayed bridge during cable removal[J].China Railway Science,2015,36(5):19―27.(in Chinese)
[13]Ke C,Song X Y.Computationally efficient down-hole drilling system dynamics modeling integrating finite element and transfer matrix[J].Journal of Dynamic Systems Measurement and Control-Transactions of the Asme,2017,139(12):121003-1―121003-8
[14]Horas C S,Alencar G,Jesus A M P D,et al.Development of an efficient approach for fatigue crack initiation and propagation analysis of bridge critical details using the modal superposition technique[J].Engineering Failure Analysis,2018,89(9):118―137.
[15]Guo W W,Xia H,Roeck G D,et al.Integral model for train-track-bridge interaction on the Sesia viaduct:Dynamic simulation and critical assessment[J].Computers&Structures,2012,112(1):205―216.
[16]Xu Y L,Li Q,Wu D J,et al.Stress and acceleration analysis of coupled vehicle and long-span bridge systems using the mode superposition method[J].Engineering Structures,2010,32(5):1356―1368.
[17]Guo W H,Xu Y L.Fully computerized approach to study cable-stayed bridge-vehicle interaction[J].Journal of Sound&Vibration,2001,248(4):745―761.
[18]Biondi B,Muscolino G,Sofi A.A substructure approach for the dynamic analysis of train-track-bridge system[J].City:Pergamon Press,Inc.,2005,83(28/29/30):2271―2281.
[19]Zhu Z,Gong W,Wang L,et al.A hybrid solution for studying vibrations of coupled train-track-bridge system[J].Advances in Structural Engineering,2017,20(11):1699―1711.
[20]朱志辉,龚威,张磊.等.基于分离迭代和耦合时变的列车-轨道-桥梁耦合系统高效动力分析混合算法[J].中国铁道科学,2018,39(1):66―74.Zhu Zhihui,Gong Wei,Zhang Lei,et al.An efficient hybrid algorithm for dynamic analysis of train-track-bridge coupled system based on separation iterative method and coupled time-varying method[J].China Railway Science,2018,39(1):66―74.(in Chinese)
[21]张攀,周昌盛,王平.轨下垫板刚度的时变特性及其影响研究[J].铁道标准设计,2015,59(9):49―52.Zhang Pan,Zhou Changsheng,Wang Ping.Study on Time Variant Characteristics and Effects of Rail Pad Stiffness[J].Railway Standard Design,2015,59(9):49―52.(in Chinese)
[22]Fryba L.Vibration of solids and structures under moving loads[M].Groningen,The Netherlands:Noordhoff International,1972.
[23]Steele C R.The finite beam with a moving load[J].Journal of Applied Mechanics,1967,34(1):111―118.
[24]Wiriyachai A,Chu K H,Garg V K.Bridge impact due to wheel and track irregularities[J].Journal of the Engineering Mechanics Division,1982,108(4):648―666.
[25]Clark R A.An investigation into the dynamic effects of railway vehicle running on corrugated rail[J].Journal of Mechanical Engineering Science,1982,24(2):65―76.
[26]Ling L,Han J,Xiao X,et al.Dynamic behavior of an embedded rail track coupled with a tram vehicle[J].Journal of Vibration&Control,2015,23(14):2355―2372.
[27]Zhang N,Xia H,Guo W W,et al.A vehicle-bridge linear interaction model and its validation[J].International Journal of Structural Stability&Dynamics,2010,10(2):335―361.
[28]Li Y L,Yang S,Xia F L,et al.Vertical dynamic response of the ballastless track on long-span plate-truss cable-stayed bridges[J].Science China Technological Sciences,2015,58(2):236―247.
[29]Liu K,Reynders E,Roeck G D,et al.Experimental and numerical analysis of a composite bridge for high-speed trains[J].Journal of Sound&Vibration,2009,320(1/2):201―220.
[30]Zhu Z,Wang L,Yu Z,et al.Non-stationary random vibration analysis of railway bridges under moving heavy-haul trains[J].International Journal of Structural Stability&Dynamics,2018,(5):1850035.
[31]刘玮,曲村.高速铁路桥上有砟轨道轨枕选型方案研究[J].高速铁路技术,2011,2(3):38―42.Liu Wei,Qu Cun.Study on selection of sleepers for ballasted track on bridges of high-speed railway[J].High Speed Railway Technology,2011,2(3):38―42.(in Chinese)
[32]李星新,田启贤,郑平伟,等.大跨度高速铁路桥梁测试与分析中的技术问题[J].桥梁建设,2009(增刊2):89―92.Li Xingxin,Tian Qixian,Zheng Weiping,et al.Technical issues in testing and analysis of long span high-speed railway bridges[J].Bridge Construction,2009(Suppl 2):89―92.(in Chinese)
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