曲线轨道参数对钢轨振动衰减率的影响研究
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摘要
建立曲线轨道解析模型,研究扣件刚度、扣件阻尼、扣件间距以及曲线轨道半径对钢轨振动衰减率的影响规律。轨道模型考虑为具有周期性离散支承的曲线Timoshenko梁,在频域内,将曲线钢轨的位移及转角表达为轨道模态的叠加,进而求解固定谐振荷载作用下曲线轨道的平面内和平面外动力响应。由于此轨道模型为无限周期性结构,将周期性结构理论应用于轨道模型的运动方程,可以在一个基本元内高效地求解轨道的动力响应。利用此模型计算固定谐振荷载作用下曲线钢轨的速度频响函数,据此计算钢轨的振动衰减率。经计算分析可知:在2 000 Hz以内,扣件刚度对钢轨振动衰减率有一定的影响,随着扣件刚度的增加,钢轨振动衰减率增大;对于100 Hz以上频段,扣件阻尼对钢轨振动衰减率有非常显著的影响,增加扣件阻尼可以显著提高钢轨振动衰减率;如果考虑全频段的钢轨振动衰减率,0.6 m扣件间距要优于0.4 m和0.8 m扣件间距;对于铁路轨道或城市轨道交通的轨道,曲线轨道半径变化对钢轨振动衰减率没有影响。
Here, an analytical model of a curved track was built to study effect laws of fasteners' stiffness, damping and spacing, and curved track radius on the rail vibration decay rate. The track model was considered as a curved Timoshenko beam with periodically discretized supports. In frequency domain, displacement and slope of the curved track were expressed as superposition of its modes, and then in-plane and out-of-plane dynamic responses of the curved track subjected to harmonic loads with fixed positions were solved. Due to the track model being an infinite periodic structure, the periodic structure theory was applied in the track model's equations of motion, so the track's dynamic response could be solved effectively within a basic element. The track model was used to calculate the velocity FRF of the curved track under harmonic loads with fixed positions, and then calculate the rail vibration decay rate. The calculation results showed that within the range of 0-2 000 Hz, fastener stiffness affects the rail vibration decay rate to a certain extent, and the rate increases with increase in fastener stiffness; within the range of larger than 100 Hz, fastener damping affects the rate very significantly, increasing fastener damping can make the rail vibration decay rate lift significantly; if considering the rail vibration decay rate in the whole frequency range, fastener spacing of 0.6 m is better than that of 0.4 m and that of 0.8 m; change in curved track radius does not affect the rail vibration decay rate for railway tracks and urban rail transit system's ones.
Here, an analytical model of a curved track was built to study effect laws of fasteners' stiffness, damping and spacing, and curved track radius on the rail vibration decay rate. The track model was considered as a curved Timoshenko beam with periodically discretized supports. In frequency domain, displacement and slope of the curved track were expressed as superposition of its modes, and then in-plane and out-of-plane dynamic responses of the curved track subjected to harmonic loads with fixed positions were solved. Due to the track model being an infinite periodic structure, the periodic structure theory was applied in the track model's equations of motion, so the track's dynamic response could be solved effectively within a basic element. The track model was used to calculate the velocity FRF of the curved track under harmonic loads with fixed positions, and then calculate the rail vibration decay rate. The calculation results showed that within the range of 0-2 000 Hz, fastener stiffness affects the rail vibration decay rate to a certain extent, and the rate increases with increase in fastener stiffness; within the range of larger than 100 Hz, fastener damping affects the rate very significantly, increasing fastener damping can make the rail vibration decay rate lift significantly; if considering the rail vibration decay rate in the whole frequency range, fastener spacing of 0.6 m is better than that of 0.4 m and that of 0.8 m; change in curved track radius does not affect the rail vibration decay rate for railway tracks and urban rail transit system's ones.
引文
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[4] BS EN 15461:2008+A1:2010.Railway applications -Noise emission-Characterisation of the dynamic properties of track sections for pass by noise measurements[S].London:BSI-British Standards Institution,2010.
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[11] WU T X.On the railway track dynamics with rail vibration absorber for noise reduction[J].Journal of Sound and Vibration,2008,309(3/4/5):739-755.
[12] SQUICCIARINI G,TOWARD M G R,THOMPSON D J.Experimental procedures for testing the performance of rail dampers[J].Journal of Sound and Vibration,2015,359:21-39.
[13] KOSTOVASILIS D,KOROMA S,HUSSEIN M F M,et al.A Comparison between the use of straight and curved beam elements for modelling curved railway tracks[C].11th International Conference on Vibration Problems,Lisbon,Portugal,2013.
[14] KOSTOVASILIS D,THOMPSON D J,HUSSEIN M F M.The effect of vertical- coupling of rails including initial curvature[C].22nd International Congress on Sound and Vibration,Florence,Italy,2015.
[15] ANG K,DAI J.Response analysis of a curved rail subject to a moving load[C].11th International Conference on Vibration Problems,Lisbon,Portugal,2013.
[16] 李克飞.基于变速及曲线车轨耦合频域解析模型的地铁减振轨道动力特性研究[D].北京:北京交通大学,2012.
[17] LI Kefei,LIU Weining,MARKINE V,et al.Analytical study on the dynamic displacement response of a curved track subjected to moving loads[J].Journal of Zhejiang University-SCIENCE A,2013,14(12):867-879.
[18] LI Kefei,LIU Weining,MARKINE V,et al.Analytical study on the vibration response of curved track subjected to moving load[C].2nd International Conference on Railway Engineering,ICRE,Beijing,China,2012:556-562.
[19] ZHANG Hougui,LIU Weining,LI Kefei,et al.Analytical solution for dynamic response of curved rail subjected to moving train[J].Journal of Vibroengineering,2014,16(4):1392-8716.
[20] GRY L,GONTIER C.Dynamic modeling of railway track:a periodic model based on a generalized beam formulation[J].Journal of Sound and Vibration,1997,199:531-558.
[21] SHENG X,LI M.Propagation constants of railway tracks as a periodic structure[J].Journal of Sound and Vibration,2007,299:1114-1123.
[22] SHENG X,JONES C J C,THOMPSON D J.Responses of infinite periodic structures to moving or stationary harmonic loads[J].Journal of Sound and Vibration,2005,282:125-149.
[23] CLOUTEAU D,ARNSTB M,AL-HUSSAINI T M,et al.Free field vibrations due to dynamic loading on a tunnel embedded in a stratified medium[J].Journal of Sound and Vibration,2005,283(1/2):173-199.
[24] DEGRANDE G,CLOUTEAU D,OTHMAN R,et al.A numerical model for groundborne vibrations from underground railway traffic based on a periodic finite element-boundary element formulation[J].Journal of Sound and Vibration,2005,293 (3/4/5):645-666.
[25] GUPTA S,LIU W F,DEGRANDE G,et al.Prediction of vibrations induced by underground railway traffic in Beijing[J].Journal of Sound and Vibration,2008,310:608-630.
[26] 马龙祥.基于周期-无限结构理论的车轨耦合及隧道-地层振动响应预测模型研究[D].北京:北京交通大学,2014.
[27] LEE J.In-plane free vibration analysis of curved Timoshenko beams by the pseudospectral method[J].International Journal KSME,2003,17(8):1156-1163.
[28] TIMOSHENKO S P.Vibration problems in engineering[M].New York:D.Van Nostrand,1955.
[29] HOWSON W P,JEMAH A K.Exact out-of-plane natural frequencies of curved timoshenko beams[J].J.Eng.Mech.,1999,125(1):19-25.
[30] BELOTSERKOVSKIY P M.Forced oscillations of infinite periodic structures[J].Vehicle System Dynamics:International Journal of Vehicle Mechanics and Mobility,1998,29:85-103.
[31] BELOTSERKOVSKIY P M.On the oscillations of infinite periodic beams subjected to a moving concentrated force[J].Journal of Sound and Vibration,1996,193:705-712.
[2] JIN Xuesong,WEN Zefeng,WANG Kaiyun,et al.Effect of a scratch on curved rail on initiation and evolution of rail corrugation[J].Tribology International,2004,37:385-394.
[3] THOMPSON D J.Railway noise and vibration:mechanisms,modelling and means of control[M].Oxford:Elsevier,2009.
[4] BS EN 15461:2008+A1:2010.Railway applications -Noise emission-Characterisation of the dynamic properties of track sections for pass by noise measurements[S].London:BSI-British Standards Institution,2010.
[5] 谷爱军,刘维宁,张厚贵,等.地铁扣件刚度和阻尼对钢轨异常波磨的影响[J].都市快轨交通,2011,24(3):17-21.GU Aijun,LIU Weining,ZHANG Hougui,et al.Impact of rail fasteners’ stiffness and damping on abnormal rail corrugation[J].Urban Rapid Rail Transit,2011,24(3):17-21.
[6] ZHANG Hougui,LIU Weining,LIU Weifeng,et al.Study on the cause and treatment of rail corrugation for Beijing metro[J].Wear,2014,317(1/2):120-128.
[7] 刘卫丰,张厚贵,孟磊,等.北京地铁采用调频式钢轨减振器抑制钢轨振动的试验研究[J].振动工程学报,2016,29(1):105-111.LIU Weifeng,ZHANG Hougui,MENG Lei,et al.A test study on suppressing rail vibration by tuned rail damper for beijing metro[J].Journal of Vibration Engineering,2016,29(1):105-111.
[8] JONES C J C,THOMPSON D J,DIEHL R J.The use of decay rates to analyze the performance of railway track in rolling noise generation[J].Journal of Sound and Vibration,2006,293(3/4/5):485-495.
[9] RYUE J,THOMPSON D J,WHITE P R,at al.Decay rates of propagating waves in railway tracks at high frequencies[J].Journal of Sound and Vibration,2009,320(4):955-976.
[10] THOMPSON D J,JONES C J C,WATERS T P,et al.A tuned damping device for reducing noise from railway track[J].Applied Acoustics,2007,68(1):43-57.
[11] WU T X.On the railway track dynamics with rail vibration absorber for noise reduction[J].Journal of Sound and Vibration,2008,309(3/4/5):739-755.
[12] SQUICCIARINI G,TOWARD M G R,THOMPSON D J.Experimental procedures for testing the performance of rail dampers[J].Journal of Sound and Vibration,2015,359:21-39.
[13] KOSTOVASILIS D,KOROMA S,HUSSEIN M F M,et al.A Comparison between the use of straight and curved beam elements for modelling curved railway tracks[C].11th International Conference on Vibration Problems,Lisbon,Portugal,2013.
[14] KOSTOVASILIS D,THOMPSON D J,HUSSEIN M F M.The effect of vertical- coupling of rails including initial curvature[C].22nd International Congress on Sound and Vibration,Florence,Italy,2015.
[15] ANG K,DAI J.Response analysis of a curved rail subject to a moving load[C].11th International Conference on Vibration Problems,Lisbon,Portugal,2013.
[16] 李克飞.基于变速及曲线车轨耦合频域解析模型的地铁减振轨道动力特性研究[D].北京:北京交通大学,2012.
[17] LI Kefei,LIU Weining,MARKINE V,et al.Analytical study on the dynamic displacement response of a curved track subjected to moving loads[J].Journal of Zhejiang University-SCIENCE A,2013,14(12):867-879.
[18] LI Kefei,LIU Weining,MARKINE V,et al.Analytical study on the vibration response of curved track subjected to moving load[C].2nd International Conference on Railway Engineering,ICRE,Beijing,China,2012:556-562.
[19] ZHANG Hougui,LIU Weining,LI Kefei,et al.Analytical solution for dynamic response of curved rail subjected to moving train[J].Journal of Vibroengineering,2014,16(4):1392-8716.
[20] GRY L,GONTIER C.Dynamic modeling of railway track:a periodic model based on a generalized beam formulation[J].Journal of Sound and Vibration,1997,199:531-558.
[21] SHENG X,LI M.Propagation constants of railway tracks as a periodic structure[J].Journal of Sound and Vibration,2007,299:1114-1123.
[22] SHENG X,JONES C J C,THOMPSON D J.Responses of infinite periodic structures to moving or stationary harmonic loads[J].Journal of Sound and Vibration,2005,282:125-149.
[23] CLOUTEAU D,ARNSTB M,AL-HUSSAINI T M,et al.Free field vibrations due to dynamic loading on a tunnel embedded in a stratified medium[J].Journal of Sound and Vibration,2005,283(1/2):173-199.
[24] DEGRANDE G,CLOUTEAU D,OTHMAN R,et al.A numerical model for groundborne vibrations from underground railway traffic based on a periodic finite element-boundary element formulation[J].Journal of Sound and Vibration,2005,293 (3/4/5):645-666.
[25] GUPTA S,LIU W F,DEGRANDE G,et al.Prediction of vibrations induced by underground railway traffic in Beijing[J].Journal of Sound and Vibration,2008,310:608-630.
[26] 马龙祥.基于周期-无限结构理论的车轨耦合及隧道-地层振动响应预测模型研究[D].北京:北京交通大学,2014.
[27] LEE J.In-plane free vibration analysis of curved Timoshenko beams by the pseudospectral method[J].International Journal KSME,2003,17(8):1156-1163.
[28] TIMOSHENKO S P.Vibration problems in engineering[M].New York:D.Van Nostrand,1955.
[29] HOWSON W P,JEMAH A K.Exact out-of-plane natural frequencies of curved timoshenko beams[J].J.Eng.Mech.,1999,125(1):19-25.
[30] BELOTSERKOVSKIY P M.Forced oscillations of infinite periodic structures[J].Vehicle System Dynamics:International Journal of Vehicle Mechanics and Mobility,1998,29:85-103.
[31] BELOTSERKOVSKIY P M.On the oscillations of infinite periodic beams subjected to a moving concentrated force[J].Journal of Sound and Vibration,1996,193:705-712.
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