基于FEM和TMM方法的轨道-隧道-土层振动耦合响应分析
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摘要
针对地铁隧道中日益增多的振动问题,基于FEM(有限元)和TMM(传递矩阵方法)技术,以上海轨道交通四号线为研究背景,探讨在移动荷载作用下轨道-隧道-土层系统的振动响应及荷载传播问题。其中在频率波数域内运用FEM模拟轨道系统响应,运用TM技术模拟土层运动,并将隧道简化为欧拉梁,利用应力应变关系将轨道系统、土层与隧道梁进行耦合。模拟数据与实测数据对比表明,该模型能较好地模拟地铁隧道中振动的传播。基于该理论模型,运用频散曲线对轨道及土层特性进行分析,从理论上讨论轨道系统与土层耦合条件下振动波传播的特殊规律,并以地表位移及土层应力为研究对象,分析不同频率条件下振动响应的差异。
A theoretical model combining the FEM(finite element method) and TMM(transfer matrix method) was presented to simulate the dynamic response induced by the moving quasi-static or harmonic load in metro line.In the model,the tunnel was simplified as an Euler beam coupled with the track and surrounding layers,where the track system was modelled by FEM while the surrounding layers were modelled by TMM.Based on this theoretical model,the dispersion characteristics of the propagating modes of vibration in the track,tunnel and ground were presented,and the response of the ground including the surface motion and ground stress were discussed in relation to the propagating wavenumbers.The influencial factors on the wave propagation in the track and tunnel were considered and some important features of the coupled system were provided.
A theoretical model combining the FEM(finite element method) and TMM(transfer matrix method) was presented to simulate the dynamic response induced by the moving quasi-static or harmonic load in metro line.In the model,the tunnel was simplified as an Euler beam coupled with the track and surrounding layers,where the track system was modelled by FEM while the surrounding layers were modelled by TMM.Based on this theoretical model,the dispersion characteristics of the propagating modes of vibration in the track,tunnel and ground were presented,and the response of the ground including the surface motion and ground stress were discussed in relation to the propagating wavenumbers.The influencial factors on the wave propagation in the track and tunnel were considered and some important features of the coupled system were provided.
引文
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[2]Cui F,Chew C H.The effectiveness of floating slab track system-Part I.Reacceptance methods[J].Applied Acoustics,2000,61:441-453.
[3]Li Z G,Wu T X.Modelling and analysis of force transmission in floating-slab track for railways[J].Proceedings of the Institution of Mechanical Engineers,Part F:Journal of Rail and Rapid Transit,2008,222:45-57.
[4]Grundmann H.The response of a layered half-space to traffic loads moving along its surface,Archive of Applied Mechanics[J].Archive of Applied Mechanics,1999,69(1):55-67.
[5]Takemiya H.Ground vibrations alongside track induced by high-speed trains:prediction and mitigation[J].Noise and Vibration from High-speed Trains,2001:347-393.
[6]Sheng X,Jones C J C,Petyt M.Ground vibration generated by a load moving along a railway track[J].Journal of Sound and Vibration,1999,228(1):129-156.
[7]Sheng X,Jones C J C,Thompson D J.A theoretical study on the influence of the track on train-induced ground vibration[J].Journal of Sound and Vibration,2004,272(3-5):909-936.
[8]Metrikine A V.Surface ground vibration due to a moving train in a tunnel:two-dimensional model[J].Journal of Sound and vibration,2000,234(1):43-66.
[9]Hussein M F M,Hunt H E M.Modelling of floating-slab track with discontinuous slab part1:response to oscillating moving loads[J].Low Frequency Noise,Vibration and Active Control,2006,25:23-39.
[10]Gupta S,Degrande G,Lombaert G.Experimental validation of a numerical model for subway induced vibrations[J].Journal of sound and vibration,2009,321(3-5):786-812.
[11]Yang Y B,Hung H H.Soil vibrations caused by underground moving trains[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,10:1633-1644.
[12]刘卫丰,刘维宁.地铁振动预测的周期性有限元一边界元耦合模型[J].振动工程学报,2009,22(5):480-485.
[13]边学成,陈云敏,胡婷.基于2.5维有限元方法模拟高速列车产生的地基振动[J].中国科学,2008,38(5):600-617.
[14]Kolsky H.Stress waves in solids[M].New York:Dover Publications,Inc.,1963.
[15]张亚军.上海地区土动剪切模量比和阻尼比的统计研究[J].世界地震工程,2010,26(2):171-175.
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