多层有砟轨道结构弹性波波动行为及带隙特性  

Elastic Wave Behavior and Band-gap Characteristics of Multi-layer Ballasted Track Structures

作　　者：张鑫浩 赵才友[2,3] 张孝娟 ZHANG Xinhao;ZHAO Caiyou;ZHANG Xiaojuan(Tangshan Graduate School,Southwest Jiaotong University,Tangshan 063000,Hebei,China;Key Laboratory of High Speed Railway Engineering,Ministry of Education,Southwest Jiaotong University,Chengdu 610031,China;School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学唐山研究生院,河北唐山063000 [2]西南交通大学高速铁路线路工程教育部重点实验室,成都610031 [3]西南交通大学土木工程学院,成都610031

出　　处：《噪声与振动控制》2022年第2期40-45,共6页Noise and Vibration Control

基　　金：高速铁路基础研究联合基金资助项目(U1734207);国家自然科学基金资助项目(51978585);四川省应用基础研究资助项目(2020YJ0214)。

摘　　要：为更好探究弹性波在有砟轨道结构中的传播特性,建立基本元胞平面波倒格矢下的多层有砟轨道波动方程,得到无限周期结构模型的频散曲线及各阶带隙,分别为:0~57.4 Hz、72.14 Hz~122.2 Hz、141.9 Hz~243.5 Hz。通过参数分析,得出结构中的局域共振带隙主要受到扣件、轨枕、道床刚度等轨下支撑的影响;Bragg带隙主要受到扣件刚度及元胞长度的影响。同时,建立有限周期数的多层有砟轨道模型求解结构的振动传递系数dB,得到在各阶带隙范围内dB值小于0,即弹性波明显衰减,验证了带隙的存在及计算的正确性。为探寻带隙机理,模拟多层有砟轨道的集中质量模型,推导出各阶带隙的边界频率计算公式及振动模式。最后,提取位于带隙范围内的60 Hz、90 Hz、200 Hz以及位于通带范围内的70 Hz、150 Hz、2 000 Hz下的钢轨及道床位移分布,对于带隙范围内的频率,钢轨及道床位移会沿着弹性波波动方向快速衰减,表现出带隙特性,且衰减速度与振动传递系数大小相符;而对于通带范围内的频率,钢轨及道床位移沿着弹性波的波动方向无明显变化或衰减,即表现出通带特性,这进一步阐释有砟轨道结构中弹性波的传播特性以及带隙对钢轨及环境振动的抑制作用。有关结论可为后续从波动角度研究轨道结构及环境振动提供新的思路及理论支撑。The propagation characteristics of elastic waves in ballasted track are explored. The wave equation of multilayer ballasted track under the reciprocal vector of basic cell plane wave is established. The dispersion curve and band gaps of infinite periodic structure model are obtained, which are 0-57.4 Hz, 72.14 Hz-122.2 Hz and 141.9 Hz-243.5 Hz respectively. Through the parameter analysis, it is found that the local resonance band gap in the structure is mainly affected by the supports beneath the rail such as fastener, sleeper and track bed stiffness;and the Bragg band gap is mainly affected by the fastener stiffness and cell length. In addition, a multi-layer ballasted track model with finite period is established to solve the vibration transfer coefficient(dB). It is found that in the range of each order band gap, the dB value is negative, namely the elastic wave has obvious attenuation, which verifies the existence of the band gap and the correctness of the calculation. In order to figure out the mechanism of band gap, the lumped mass model of the multi-layer ballasted track is simulated, and the boundary frequency calculation formula and vibration mode of each order band gap are derived. Finally, the rail and ballast displacement distributions at the frequencies of 70 Hz, 150 Hz and 2 000 Hz within the passband and at the frequencies of 60 Hz, 90 Hz and 200 Hz within the band gap are extracted. For the frequencies in the range of band gap, the displacements of rail and ballast attenuate rapidly in the elastic wave propagation direction, which shows the characteristic of band gap, and the attenuation rate is consistent with the vibration transmission coefficient. While for the frequencies in the range of passband, the displacements of rail and ballast have no obvious change or attenuation in the wave propagation direction,showing the characteristic of passband. The above research results further explain the propagation characteristics of elastic waves in multi-layer ballasted track structure and the restraint

关 键 词：振动与波 多层有砟轨道 平面波展开法 弹性波 带隙 周期结构 环境振动 

分 类 号：U211.3[交通运输工程—道路与铁道工程]