基于能量泛函变分原理的三层有砟轨道垂向振动带隙分析  

Band-gap Analysis of Vertical Vibration of Three-layer Ballast Track Structure Based on Energy Functional Variational Principle

作　　者：冯青松[1] 廖宝亮 郭文杰 付景文 陆建飞[2] FENG Qingsong;LIAO Baoliang;GUO Wenjie;FU Jingwen;LU Jianfei(Engineering Research Center of Railway Environment Vibration and Noise,East China Jiaotong University,Nanchang 330013,China;Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]华东交通大学铁路环境振动与噪声教育部工程研究中心,江西南昌330013 [2]江苏大学土木工程学院,江苏镇江212013

出　　处：《铁道学报》2022年第4期96-103,共8页Journal of the China Railway Society

基　　金：国家自然科学基金(52178423,52068029,51878277);江西省重点研发计划(20192BBE50008);江西省主要学科学术和技术带头人培养计划(20194BCJ22008);江西省青年科学基金(20202BABL214049);中国博士后科学基金(2021M690997);江西省教育厅科学技术研究项目(190339)。

摘　　要：客货混运铁路在我国分布较广且具有明显周期特征,研究其弹性波传播特性对于轨道结构振动控制具有重要意义。以有砟轨道结构为研究对象,建立三层周期性有砟轨道结构,并提出一种基于能量泛函变分原理和平面波级数展开的混合方法,用以求解轨道结构的带隙特性。与有限元软件COMSOL仿真结果对比验证了混合方法的准确性。此外,还研究了刚度对带隙起止频率的影响规律,并从机理上解释了其成因。所提出的能量-平面波级数混合方法主要从能量的角度进行分析,为周期性轨道结构弹性波传播特性的求解提供了新的思路。Mixed passenger-freight railway is widely distributed in China and has obvious periodic characteristics.The investigation of its elastic wave propagation characteristics is of great significance for the vibration control of track structures.In this paper,based on the study of a ballast track structure,a three-layer periodic ballast track structure was established.A hybrid method based on the energy functional variational principle and plane wave series expansion was proposed to solve the band-gap characteristics of the structure.Compared with the simulation results of finite element software COMSOL,the accuracy of the hybrid method was verified.In addition,the influence of stiffness on the starting and cut-off frequencies of band-gaps was also studied,and their causes were explained from the aspect of mechanism.The method proposed in this paper mainly made analysis from the perspective of energy,which provides new ideas for solving the elastic wave propagation characteristics of periodic track structures.

关 键 词：有砟轨道结构 能量泛函变分原理 平面波级数 周期结构 振动带隙 

分 类 号：U213.2[交通运输工程—道路与铁道工程]