有砟轨道双轨模型振动带隙理论分析  

Analysis of the vibration band-gaps of bouble-rail phononic crystal model for ballast track

作　　者：梁玉雄 冯青松[1] 陆建飞[2] 杨舟 张凌 LIANG Yuxiong;FENG Qingsong;LU Jianfei;YANG Zhou;ZHANG Ling(State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,China;Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]华东交通大学轨道交通基础设施性能监测与保障国家重点实验室,江西南昌330013 [2]江苏大学土木工程与力学学院,江苏镇江212013

出　　处：《铁道科学与工程学报》2023年第4期1326-1336,共11页Journal of Railway Science and Engineering

基　　金：国家自然科学基金资助项目(52178423,52068029,51878277)。

摘　　要：现有的轨道结构振动分析模型通常根据轨道结构对称性将其简化为单根轨道的动力学模型,对其频散特性、振动衰减率进行分析。然而,单轨模型未能充分体现实际铁路中由2条轨道固定在轨枕上通过扣件连接形成的耦合特点,也忽略了振动波沿着轨枕横向传播时带来的差异。为了充分考虑钢轨和轨枕之间的空间耦合效应对有砟轨道振动带隙的影响,采用传递矩阵法将有砟轨道中的2根钢轨简化为欧拉梁,将道砟和扣件简化为连接弹簧,将轨枕简化为温克尔地基梁,建立有砟轨道结构的声子晶体双轨模型(DRPC);运用Fortran编制计算程序,对有砟轨道的振动带隙进行分析,并与仅考虑单根轨道的声子晶体单轨模型(SRPC)分析结果进行对比分析。分析结果表明:单轨模型的6种特征波包含在双轨模型的12种特征波中,且双轨模型其中一根钢轨的特征波带隙特性与相对应的单轨模型特征波带隙基本接近,而另一根钢轨的特征波带隙的中心位置和带隙宽度则较为不同;2种模型中与横向、扭转和平面内弯曲振动相关的特征波带隙特效差别较为明显,因此采用双轨模型能更精确地分析与横向、扭转和平面内弯曲振动相关的特征波带隙特性,弥补单轨模型的在空间效应简化上的不足,可更为精确地考虑与空间效应相关的各类特征波的传播特性。Existing vibration analysis models for track structure often simplify the dynamic model of the track structure to a single rail based on the symmetry of the track structure for analyzing its frequency dispersion characteristics and vibration attenuation rate.However,the single rail model fails to fully reflect the coupling characteristics of the two rails fixed on the sleepers by fasteners in actual railways,and ignores the differences in vibration wave propagation when waves propagate transversely along the sleepers.To fully consider the effect of the spatial coupling effect between the rail and the sleeper on the vibrational band gap of the ballast track,a double-rail phononic crystal(DRPC)model that consisted of two parallel rails fastened on equally spaced sleepers supported by ballast was proposed.The transfer matrix method was used to simplify the two rails in the ballasted track as Euler beams.The ballast and fasteners as connecting springs,and the sleepers as Winkler foundation beams,and a double rail phononic crystal model(DRPC)of the ballasted track structure were established.A Fortran program was used to analyze the vibration bandgap of the ballasted track,and the results were compared with those of the phononic crystal single rail model(SRPC)that only considers a single rail.The results show that the 6 characteristic waves of the SRPC model are included in the 12 characteristic waves of the DRPC model.The band-gaps of the left rail in DRPC model are basically close to the SRPC model,the central positions,and widths of the band gaps of waves in the right track of the DRPC model are different from the SRPC model.The band gaps related the transverse,torsion and in-plane bending vibration are quite different between the two models.The DRPC model can better analyze the propagation characteristics of various characteristic waves related to the spatial vibration such as the transverse,torsion and in-plane bending vibration.The DRPC model can amend the shortcomings of the spatial simplify of the SRPC model,an

关 键 词：传递矩阵法 有砟轨道 双轨声子晶体模型 单轨声子晶体模型 带隙 

分 类 号：U213[交通运输工程—道路与铁道工程]