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一維六方準晶納米板中Lamb波特性研究

王鑫鑫 禹建功 張博 劉燦燦 王現輝

王鑫鑫, 禹建功, 張博, 劉燦燦, 王現輝. 一維六方準晶納米板中Lamb波特性研究[J]. 工程力學, 2023, 40(10): 213-221. doi: 10.6052/j.issn.1000-4750.2022.01.0089
引用本文: 王鑫鑫, 禹建功, 張博, 劉燦燦, 王現輝. 一維六方準晶納米板中Lamb波特性研究[J]. 工程力學, 2023, 40(10): 213-221. doi: 10.6052/j.issn.1000-4750.2022.01.0089
WANG Xin-xin, YU Jian-gong, ZHANG Bo, LIU Can-can, WANG Xian-hui. INVESTIGATION ON LAMB WAVE CHARACTERISTICS IN ONE-DIMENSIONAL HEXAGONAL QUASI-CRYSTAL NANO PLATES[J]. Engineering Mechanics, 2023, 40(10): 213-221. doi: 10.6052/j.issn.1000-4750.2022.01.0089
Citation: WANG Xin-xin, YU Jian-gong, ZHANG Bo, LIU Can-can, WANG Xian-hui. INVESTIGATION ON LAMB WAVE CHARACTERISTICS IN ONE-DIMENSIONAL HEXAGONAL QUASI-CRYSTAL NANO PLATES[J]. Engineering Mechanics, 2023, 40(10): 213-221. doi: 10.6052/j.issn.1000-4750.2022.01.0089

一維六方準晶納米板中Lamb波特性研究

doi: 10.6052/j.issn.1000-4750.2022.01.0089
基金項目: 國家自然科學基金項目(12102131,51975189);河南理工大學博士基金項目(B2021-32);中國博士后科學基金項目(2021M701102)
詳細信息
    作者簡介:

    王鑫鑫(1998?),男,河南許昌人,碩士生,主要從事準晶納米結構中彈性波研究(E-mail: wxx2663965124@163.com)

    禹建功(1975?),男,河南開封人,教授,博士,博導,主要從事智能材料結構中波動與振動研究(E-mail: jiangongyu@126.com)

    劉燦燦(1995?),男,河南周口人,博士生,主要從事納米結構中彈性波研究(E-mail: hpuliucancan@163.com )

    王現輝(1985?),男,河南許昌人,講師,博士,主要從事復合材料結構中彈性波研究(E-mail: wxhhpu@163.com)

    通訊作者:

    張 博(1993?),男,河南蘭考人,講師,博士,主要從事復合材料結構中彈性波研究(E-mail: bozhanghpu@163.com)

  • 中圖分類號: O347.4

INVESTIGATION ON LAMB WAVE CHARACTERISTICS IN ONE-DIMENSIONAL HEXAGONAL QUASI-CRYSTAL NANO PLATES

  • 摘要: 準晶納米結構在工程中經常承受以彈性波為代表的動態工作載荷,為深入研究其動態失效機制,研究了一維六方準晶納米板中Lamb波的波動特性?;谛拚呐紤碚?,推導出Bak模型下Lamb波的波動控制方程,使用勒讓德正交多項式方法(LOPM)求解該動力學方程,計算得到其頻散曲線和位移分布。研究了聲子場和相位子場尺寸效應、聲-相耦合效應對波動特性的影響。結果表明:尺寸效應使聲子模態和相位子模態相速度增大;聲-相耦合效應顯著地增大了聲子模態中的相位子位移振幅和相位子模態中的聲子位移振幅。研究結果為準晶納米結構的設計和無損檢測奠定了一定的理論基礎。
  • 圖  1  水平無限大的一維六方準晶納米板示意圖

    Figure  1.  Schematic diagram of an infinite one-dimensional hexagonal quasi-crystal nano plate

    圖  2  氮化鋁偶應力板中Lamb波的頻散曲線

    Figure  2.  Dispersion curves of Lamb waves in an aluminum nitride couple stress plate

    圖  3  準晶偶應力板和晶體偶應力板中相速度頻散曲線

    Figure  3.  Phase velocity dispersion curves of quasi-crystal couple stress plates and corresponding crystal couple stress plates

    圖  4  kh=3,聲-相耦合系數Ri增大時前3階模態相速度曲線

    Figure  4.  Phase velocity of the first three modes with enlarged phonon-phason coupling coefficients Ri as kh=3

    圖  5  L2=0.1,L1變化時準晶偶應力板中頻散曲線

    Figure  5.  Dispersion curves for quasi-crystal couple stress plates with different L1 as L2=0.1

    圖  6  L1=0.1,L2變化時準晶偶應力板中頻散曲線

    Figure  6.  Dispersion curves for quasi-crystal couple stress plates with different L2 as L1=0.1

    圖  7  Ri被增大到10倍時,準晶偶應力板中P0和A0模態的頻散曲線

    Figure  7.  Dispersion curves of P0 and A0 modes in quasi-crystal couple stress plates as Ri are increased to 10 times

    圖  8  kh=2時,Ri變化時P0模態的聲子和相位子位移分布

    Figure  8.  Phonon and phason displacement distributions of P0 mode with different Ri when kh=2

    圖  9  kh=2時,Ri變化時A0模態的聲子和相位子位移分布

    Figure  9.  Phonon and phason displacement distributions of A0 mode with different Ri when kh=2

    圖  10  kh=2時,A0模態聲子和相位子應力分布

    Figure  10.  Phonon and phason stress distributions of A0 mode when kh=2

    表  1  一維六方準晶納米板的材料參數[28]

    Table  1.   Material parameters of one-dimensional hexagonal quasi-crystal nano plate[28]

    材料參數數值材料參數數值
    聲子場彈性常數C11/GPa234.33聲子場彈性常數C13/GPa66.63
    聲子場彈性常數C33/GPa232.22聲子場彈性常數C44/GPa70.19
    聲子場彈性常數C55/GPa70.19聲子場彈性常數C66/GPa88.46
    相位子場彈性常數K1/GPa122相位子場彈性常數K2/GPa24
    聲-相耦合系數R1/GPa0.8846聲-相耦合系數R2/GPa0.8846
    聲-相耦合系數R3/GPa0.8846材料密度ρ(kg·m?3)4186
    下載: 導出CSV

    表  2  前2階聲子模態和前2階相位子模態的相速度Vph

    Table  2.   Phase velocity Vph of the first two phonon modes and the first two phason modes /(km·s?1)

    模態無量綱波數khM=9M=10M=11M=12
    P012.397 112.397 112.397 112.397 11
    52.467 362.467 362.467 362.467 36
    102.676 492.676 492.676 492.676 49
    P1117.132 3017.132 3017.132 3017.132 30
    54.211 324.211 324.211 324.211 32
    103.190 843.190 843.190 843.190 84
    A011.815 791.815 781.815 781.815 78
    53.785 423.785 313.785 303.785 30
    104.498 434.498 424.498 404.498 40
    S017.144 187.144 187.144 187.144 18
    55.181 135.18105.181 005.181 00
    104.851 474.851 184.851 104.851 10
    下載: 導出CSV

    黑人大屌丝逼逼
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  • 收稿日期:  2022-01-18
  • 修回日期:  2022-06-07
  • 網絡出版日期:  2022-06-17
  • 刊出日期:  2023-10-10

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