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双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配

陕耀 李欣然 周顺华

陕耀, 李欣然, 周顺华. 双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配. 力学学报, 2023, 55(5): 1124-1137 doi: 10.6052/0459-1879-22-573
引用本文: 陕耀, 李欣然, 周顺华. 双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配. 力学学报, 2023, 55(5): 1124-1137 doi: 10.6052/0459-1879-22-573
Shan Yao, Li Xinran, Zhou Shunhua. The mode and scattered energy distribution of guided waves propagating in two coupled plane-strain layers with rigid base. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1124-1137 doi: 10.6052/0459-1879-22-573
Citation: Shan Yao, Li Xinran, Zhou Shunhua. The mode and scattered energy distribution of guided waves propagating in two coupled plane-strain layers with rigid base. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1124-1137 doi: 10.6052/0459-1879-22-573

双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配

doi: 10.6052/0459-1879-22-573
基金项目: 国家自然科学基金资助项目(51708424)
详细信息
    通讯作者:

    陕耀, 副教授, 主要研究方向为轨道交通线路系统动力学. E-mail: shanyao@tongji.edu.cn

  • 中图分类号: O343.1

THE MODE AND SCATTERED ENERGY DISTRIBUTION OF GUIDED WAVES PROPAGATING IN TWO COUPLED PLANE-STRAIN LAYERS WITH RIGID BASE

Funds: The project was supported by the (12345678)and (9876543)
  • 摘要: 过渡段动力稳定性问题已成为制约400 km/h及以上高铁路基设计的关键难题, 亟需从波动和能量的角度探究由基础非均匀引发的线路系统动力响应放大机理. 文章将轨下基础简化为上表面自由、底端固定的刚性基弹性层, 将高铁过渡段车致弹性波传播问题提炼为非均匀介质刚性基弹性层中波的散射问题, 建立双介质耦合刚性基弹性层平面应变模型, 优化该类波导结构频散方程在复平面求根方法, 并结合岩土类介质特征展开刚性基弹性层频散分析, 以明确其多模式导波特性及散射能量分配, 最后, 围绕弹性层厚度、刚度比等影响因素开展对比分析. 结果表明: 刚性基弹性层各模式导波均具有截止频率, 弹性层厚度越小, 杨氏模量越大, 各阶导波模式的截止频率越高; 入射波在双介质刚性基弹性层发生散射后, 透射场基阶模式导波会占据主体能量, 随着高阶导波模式被逐一激发, 反射场及透射场高阶模式能量占比会在全频率范围呈现“此消彼长”状态; 交换两侧弹性层材料, 改变弹性层厚度及两弹性层刚度比不会显著改变能量分布规律, 但总体来看, 能量更易集中在较软侧弹性层中, 各模式导波在激发初始频段会更为活跃, 可分配到更多能量.

     

  • 图  1  高速铁路路桥过渡段形式[5]

    Figure  1.  Bridge-embankment transition zone configuration of high-speed railway[5]

    图  2  双介质耦合刚性基弹性层平面应变模型

    Figure  2.  Plane-strain model of two medium coupling elastic layers with rigid base

    图  3  刚性基弹性层波导结构平面应变模型

    Figure  3.  Plane-strain model of waveguide structure of elastic layer with rigid base

    图  4  频散方程$ {\text{Det(}}{k_x}) = 0 $求解流程图

    Figure  4.  Flow chart of the solution of dispersion equation $ {\text{Det(}}{k_x}) = 0 $

    图  5  复平面网格划分示意

    Figure  5.  Mesh generation on complex plane

    图  6  水平波数$ {k_x} $计算结果及验证

    Figure  6.  Calculation results and verification of horizontal wave number $ {k_x} $

    图  7  钢介质刚性基弹性层频散曲线

    Figure  7.  Dispersion curve of rigid base elastic layer with steel medium

    图  8  刚性基弹性层导波模式相速度

    Figure  8.  Phase velocity of guided wave modes in rigid base elastic layer

    图  9  刚性基弹性层导波模式群速度

    Figure  9.  Group velocity of guided wave modes in rigid base elastic layer

    图  10  垂直界面处位移连续性验证

    Figure  10.  Verification of displacement continuity at vertical interface

    图  11  各场传播模式导波分配总能量占比

    Figure  11.  Proportion of total energy distributed by propagating guided wave modes in each field

    图  12  基阶及高阶传播模式导波分配能量占比

    Figure  12.  Proportion of energy distribution of the fundamental and higher propagating guided wave modes

    图  13  材料交换后各场传播模式导波分配能量占比

    Figure  13.  Proportion of energy distributed by propagating guided wave modes in each field after exchanging material

    图  14  不同弹性层厚度下各场传播模式导波分配能量占比

    Figure  14.  Proportion of energy distributed by propagating guided wave modes in each field under different elastic layer thicknesses

    14  不同弹性层厚度下各场传播模式导波分配能量占比 (续)

    14.  Proportion of energy distributed by propagating guided wave modes in each field under different elastic layer thicknesses (continued)

    图  15  两弹性层不同刚度比下各场传播模式导波分配能量占比

    Figure  15.  Proportion of energy distributed by propagating guided wave modes in each field under different stiffness ratios of two elastic layers

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出版历程
  • 收稿日期:  2022-12-03
  • 录用日期:  2023-04-24
  • 网络出版日期:  2023-04-25
  • 刊出日期:  2023-05-18

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