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

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.