轴向温度力影响下周期离散支承钢轨竖向振动特性分析
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摘要
建立轴向温度力作用下无缝线路轨道结构周期离散支承梁模型,其中钢轨采用Timoshenko梁模拟,轨枕考虑为质量块,轨下支承结构对钢轨的支承作用通过动力柔度矩阵进行模拟。通过周期结构波数有限元法,分析得到周期离散支承钢轨的频散特性及位移响应。分析周期离散支承钢轨各阶共振频率与轴向温度力的关系,并探讨轨枕间距的影响。分析结果表明:在0~5 000Hz范围内,周期离散支承钢轨竖向振动各阶共振频率均随轴向拉力的增加而增大,随轴向压力的增加而减小,且共振频率越高,其受轴向温度力影响越明显。其中,共振频率D(1 080Hz)、G(2 947Hz)、H(4 657Hz)受轴向温度力的影响最明显,可作为无缝线路钢轨内部温度力大小的主要评价指标。轨枕间距对各阶共振频率有较大影响,分析时需先确定轨枕间距实际值。
A periodic discretely supported beam model of continuously welded railway(CWR)track structure under axial temperature force was established,where the rail was simulated by a Timoshenko beam and the sleeper was considered as mass block.The supporting action of the supported structure under the rail was simulated by the dynamic receptance matrix.Through the wavenumber finite element method for periodic structure,the displacement response and dispersion characteristics of the periodic discretely supported rail were obtained.The relationship between the axial temperature force and the resonate frequencies of each order of the periodical discretely supported rail was analyzed and the influence of the sleeper spacing was also discussed.The results show that,in the range of 0~5 000 Hz,the resonate frequency of each order increases with the increase of the axial tension force and decreases with the increase of the axial compressive stress.The higher the resonance frequency is,the more obvious the influence of axial temperature force will be.The resonate frequency D(1 080 Hz),G(2 947 Hz)and H(4 657 Hz)are most obviously affected by the axial temperature force and may be used as the main indexes for evaluating the temperature force inside the rail.Given the relatively high effect of the sleeper spacing on the resonance frequency of each order,the actual sleeper spacing must be determined first during analysis.
A periodic discretely supported beam model of continuously welded railway(CWR)track structure under axial temperature force was established,where the rail was simulated by a Timoshenko beam and the sleeper was considered as mass block.The supporting action of the supported structure under the rail was simulated by the dynamic receptance matrix.Through the wavenumber finite element method for periodic structure,the displacement response and dispersion characteristics of the periodic discretely supported rail were obtained.The relationship between the axial temperature force and the resonate frequencies of each order of the periodical discretely supported rail was analyzed and the influence of the sleeper spacing was also discussed.The results show that,in the range of 0~5 000 Hz,the resonate frequency of each order increases with the increase of the axial tension force and decreases with the increase of the axial compressive stress.The higher the resonance frequency is,the more obvious the influence of axial temperature force will be.The resonate frequency D(1 080 Hz),G(2 947 Hz)and H(4 657 Hz)are most obviously affected by the axial temperature force and may be used as the main indexes for evaluating the temperature force inside the rail.Given the relatively high effect of the sleeper spacing on the resonance frequency of each order,the actual sleeper spacing must be determined first during analysis.
引文
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[17]SHENG X,LI M H.Propagation Constants of Railway Tracks as a Periodic Structure[J].Journal of Sound and Vibration,2007,299(4/5):1114-1123.
[18]孙方遒,谷爱军,刘维宁.钢轨长实体模型在不同频段的振动及传递特性分析[J].铁道学报,2013,35(2):81-86.SUN Fangqiu,GU Aijun,LIU Weining.Study on Vibration and Transmission Characteristics of Long Solid Rail Models under Different Frequencies[J].Journal of the China Railway Society,2013,35(2):81-86.
[2]刘维宁,马龙祥,姜博龙,等.浮置板轨道动力响应分析的广义波数法[J].中国铁道科学,2016,37(1):31-38.LIU Weining,MA Longxiang,JIANG Bolong,et al.Generalized Wavenumber Method for Dynamic Response Analysis of Floating Slab Track[J].China Railway Science,2016,37(1):31-38.
[3]辛涛,高亮,郑晓莉.车辆-有砟轨道-桥梁系统动力分析模型及验证[J].北京交通大学学报,2011,35(3):72-76.XIN Tao,GAO Liang,ZHENG Xiaoli.Dynamic Analysis Model and Verification for Vehicle-ballast Track-bridge System[J].Journal of Beijing Jiaotong University,2011,35(3):72-76.
[4]向俊,赫丹,曾京.高速列车作用下不同类型无砟轨道振动响应分析[J].机械工程学报,2010(16):29-35.XIANG Jun,HE Dan,ZENG Jing.Investigation on Dynamic Responses of Different Type Ballastless Tracks under High-speed Train[J].Journal of Mechanical Engineering,2010(16):29-35.
[5]方锐,肖新标,房建英,等.轨道结构参数对钢轨和轨枕振动特性的影响[J].铁道学报,2011,33(3):71-76.FANG Rui,XIAO Xinbiao,FANG Jianying,et al.Effect of Structure Parameters of Railway Track on Dynamic Behavior of Rail and Sleeper[J].Journal of the China Railway Society,2011,33(3):71-76.
[6]HOANG T,DUHAMEL D,FORET G,et al.Dynamic Response of Railway Tracks in Tunnel[C]//ECCOMAS11th World Congress on Computational Mechanics.Barcelona,2014:01118265.
[7]BROWN G P,BYRNE K P.Determining the Response of Infinite,One-dimensional,Non-uniform Periodic Structures by Substructuring Using Waveshape Coordinates[J].Journal of Sound and Vibration,2005,287(3):505-523.
[8]MAZILU T,DUMITRIU M,TUDORACHE C,et al.New Method for Calculating Response of a Periodic Structure Due to Moving Loads[J].Proceedings of the Romanian Academy-Series A:Mathematics,Physics,Technical Sciences,Information Science,2010,11(4):340-346.
[9]RACHID L,LECHEHEB M,BONNET G.Green's Function and Bloch Theory for the Analysis of the Dynamic Response of a Periodically Supported Beam to a Moving Load[J].Journal of Physics Conference Series,2012,382(1):012053.
[10]GARCIA-PALACIOS J,SAMARTIN A,MELIS M.Analysis of the Railway Track as a Spatially Periodic Structure[J].Proceedings of the Institution of Mechanical Engineers-Part F:Journal of Rail and Rapid Transit,2012,226(2):113-123.
[11]罗雁云,朱剑月,冯奇.不同温度力下无缝线路钢轨振动特性分析[J].力学季刊,2006,27(2):279-285.LUO Yanyun,ZHU Jianyue,FENG Qi.CWR Vibration Characteristic Analysis under Different Temperature Force[J].Chinese Quarterly of Mechanics,2006,27(2):279-285.
[12]董国鹏,朱剑月,罗雁云.无缝线路钢轨振动特性谐响应有限元分析[J].科学技术与工程,2005,5(20):1518-1521.DONG Guopeng,ZHU Jianyue,LUO Yanyun.FEM Analysis on CWR Vibration Characteristic through Harmonic Response Way[J].Science Technology and Engineer,2005,5(20):1518-1521.
[13]金寿延,朱剑月,罗雁云,等.无缝线路轨道的温度力与振动特性关系的研究[J].机械强度,2002,24(1):144-147.JIN Shouyan,ZHU Jianyue,LUO Yanyun,et al.Study on the Relation between Temperature Force of Continuous Welded Rail Track and Vibration Characteristic[J].Journal of Mechanical Strength,2002,24(1):144-147.
[14]吴丹.无缝线路受温度力作用下的振动特性影响研究[D].上海:同济大学,2007.
[15]AIKAWA A,SAKAI H,ABE K.Numerical and Experimental Study on Measuring Method of Rail Axial Stress of Continuous Welded Rails Based on Use of Resonant Frequency[J].Quarterly Report of Rtri,2013,54(2):118-125.
[16]雷晓燕,圣小珍.现代轨道理论研究[M].北京:中国铁道出版社,2006.
[17]SHENG X,LI M H.Propagation Constants of Railway Tracks as a Periodic Structure[J].Journal of Sound and Vibration,2007,299(4/5):1114-1123.
[18]孙方遒,谷爱军,刘维宁.钢轨长实体模型在不同频段的振动及传递特性分析[J].铁道学报,2013,35(2):81-86.SUN Fangqiu,GU Aijun,LIU Weining.Study on Vibration and Transmission Characteristics of Long Solid Rail Models under Different Frequencies[J].Journal of the China Railway Society,2013,35(2):81-86.