基于能量泛函变分原理的无砟轨道垂向振动带隙分析  

Band-gap Analysis of Vertical Vibration of Ballastless Track Based on Energy Functional Variational Principle

作　　者：冯青松[1] 廖宝亮 郭文杰 杨舟 付景文 陆建飞[2] FENG Qingsong;LIAO Baoliang;GUO Wenjie;YANG Zhou;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]江苏大学土木工程与力学学院,江苏镇江212013

出　　处：《铁道学报》2022年第7期98-106,共9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);中国博士后科学基金(2021M690997);轨道交通基础设施性能监测与保障国家重点实验室自主课题(HJGZ2021211)。

摘　　要：以我国CRTSⅢ型无砟轨道结构为研究对象,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,用于计算周期性无砟轨道结构振动带隙。将求解微分方程边值问题转化为泛函极值问题,易于解决组合结构的耦合问题;利用平面波级数构造钢轨位移函数,使其能够满足周期边界条件;结合切比雪夫级数构造轨道板位移场;最终建立整个复杂系统的总能量泛函,变分后即可得到特征方程,进而求解出无砟轨道结构的垂向振动带隙。对比分析有限元仿真结果和简化模型结果,验证了本文方法准确可靠,通过机理分析揭示了带隙成因;解决了传统解析方法囿于直接求解微分方程组以及难于对轨道板建模的问题,为不同类型轨道结构带隙计算提供了新思路。Based on the case study of CRTSⅢballastless track structure in China,a hybrid method based on energy functional variational principle and plane wave series expansion was proposed to calculate the vibration band gap of periodic ballastless track structure.On the one hand,the problem of solving the boundary value problem of differential equations was converted into a functional extremum problem,which is easy to solve the coupling problem of composite structure.On the other hand,using plane wave series to construct the displacement function of rail can satisfy the periodic boundary condition.In addition,the Chebyshev series was combined to construct the displacement field of the track slab.Finally,the total energy functional of the whole complex system was established,and the characteristic equation can be obtained after the variation,to solve the vertical vibration bandgap of ballastless track structure.The comparison with the results of the finite element simulation and simplified model shows that the method in this paper is accurate and reliable,and the cause of band gap is revealed through mechanism analysis.The method in this paper solves the limits of the traditional analytical method to solve the differential equations directly and eliminates the difficulty to model the track slab,and provides a new idea about the band gap calculation of various types of track structures.

关 键 词：周期性无砟轨道结构 能量泛函变分原理 平面波级数 切比雪夫级数 振动带隙 

分 类 号：U213.2[交通运输工程—道路与铁道工程]