低速冲击下负泊松比蝴蝶形蜂窝夹芯板的动力响应

余阳 付涛

余阳, 付涛. 低速冲击下负泊松比蝴蝶形蜂窝夹芯板的动力响应[J]. 爆炸与冲击, 2023, 43(7): 073103. doi: 10.11883/bzycj-2023-0019
引用本文: 余阳, 付涛. 低速冲击下负泊松比蝴蝶形蜂窝夹芯板的动力响应[J]. 爆炸与冲击, 2023, 43(7): 073103. doi: 10.11883/bzycj-2023-0019
YU Yang, FU Tao. Dynamic response of a sandwich panel cored by butterfly-shaped honeycombs with negative Poisson’s ratio to low-velocity impact[J]. Explosion And Shock Waves, 2023, 43(7): 073103. doi: 10.11883/bzycj-2023-0019
Citation: YU Yang, FU Tao. Dynamic response of a sandwich panel cored by butterfly-shaped honeycombs with negative Poisson’s ratio to low-velocity impact[J]. Explosion And Shock Waves, 2023, 43(7): 073103. doi: 10.11883/bzycj-2023-0019

低速冲击下负泊松比蝴蝶形蜂窝夹芯板的动力响应

doi: 10.11883/bzycj-2023-0019
基金项目: 国家自然科学基金(52205105);云南省基础研究专项(202101AU070160, 202201AT070145)
详细信息
    作者简介:

    余 阳(1997- ),男,硕士研究生,yy37643562@126.com

    通讯作者:

    付 涛(1987- ),男,博士,讲师,ftkmust@126.com

  • 中图分类号: O347

Dynamic response of a sandwich panel cored by butterfly-shaped honeycombs with negative Poisson’s ratio to low-velocity impact

  • 摘要: 为了研究负泊松比蝴蝶形蜂窝夹芯板在低速冲击下的动力学响应,采用质量-弹簧模型获得了冲击器与蜂窝夹芯板之间的接触力,同时基于哈密顿原理和一阶剪切变形理论推导了负泊松比蝴蝶形蜂窝夹芯板的运动方程,采用Navier法和Duhamel积分对蜂窝板的振动位移进行了理论解析求解。在理论验证方面,蜂窝夹芯板前5阶固有频率的数值模拟结果与理论模型计算结果的最大相对误差为6.52%,蜂窝夹芯板中心最大横向位移的数值模拟结果与理论模型计算结果的最大相对误差为6.84%,理论模型求解的接触力与文献得到的接触力的最大相对误差为8%,验证了理论模型的有效性。结果表明,随着球形冲击器冲击速度的递增,蜂窝夹芯板的最大横向位移呈现递增的规律。而在相同冲击载荷下,蜂窝夹芯板的抗冲击特性随着胞元壁厚的增大而增强,随着胞元角度的增大而减弱;随着负泊松比蝴蝶形蜂窝夹芯板长宽比以及夹芯层与顶部蒙皮层的高度比的增大,蜂窝夹芯板的横向位移减小,冲击器与蜂窝夹芯板之间的接触力增大。当蜂窝夹芯板的宽长比从1∶1变化到1∶2时,蜂窝夹芯板最大横向位移减小6.1%;当顶部蒙皮层与蜂窝芯层的高度比从1∶6变化到1∶14时,蜂窝夹芯板的最大横向位移减小5.4%,这表明蜂窝夹芯板的抗冲击性能增强,吸能效果明显。
  • 图  1  蜂窝夹芯板和胞元结构示意图

    Figure  1.  Structure schematic diagram of the honeycomb sandwich panel and the unit cell

    图  2  球形冲击器与蜂窝夹芯板接触的等效理论模型

    Figure  2.  An equivalent theoretical model of contact between the spherical impactor and the sandwich panel

    图  3  有限元数值建模的网格划分

    Figure  3.  Finite element numerical modeling meshing

    图  4  蝴蝶形蜂窝夹芯板低速冲击有限元模型

    Figure  4.  The finite element model for the butterfly-shaped honeycomb sandwich panel subjected to low-velocity impact

    图  5  接触力随时间的变化

    Figure  5.  Variation of contact force with time

    图  6  胞元几何尺寸对蝴蝶形蜂窝夹芯板动力响应的影响

    Figure  6.  Influences of the unit cell geometry parameters on dynamic responses of the butterfly-shaped honeycomb sandwich panel

    图  7  顶部蒙皮层与夹芯层的高度比对蝴蝶形蜂窝夹芯板动力响应的影响

    Figure  7.  Influences of the height ratio of the top skin layer to the sandwich layer on dynamic responses of the butterfly-shaped honeycomb sandwich panel

    图  8  宽长比对蝴蝶形蜂窝夹芯板动力响应的影响

    Figure  8.  Influences of the width-length ratios on dynamic responses of the butterfly-shaped honeycomb sandwich panel

    表  1  网格尺寸对一阶固有频率计算结果的影响

    Table  1.   Influences of mesh size on the calculated results of the first-order natural frequency

    网格尺寸/mm频率/Hz
    15.0719.26
    12.5699.18
    10.0696.14
    7.5692.37
    5.0691.25
    下载: 导出CSV

    表  2  蝴蝶形蜂窝夹芯板的前5阶固有频率

    Table  2.   The first five order natural frequencies of the butterfly-shaped honeycomb sandwich panel

    阶数频率/Hz
    理论模型解有限元解
    1646.17691.25
    21597.40163.75
    31648.401706.70
    42570.502629.30
    53181.903200.80
    下载: 导出CSV

    表  3  低速冲击下蜂窝夹芯板中心网格尺寸对中心最大横向位移计算结果的影响

    Table  3.   Influence of center grid size on the calculated maximum lateral displacement of the sandwich panel center under low-velocity impact

    网格尺寸/mm中心最大横向位移/mm
    10.00.1928
    5.00.2129
    2.50.2218
    1.00.2516
    0.50.2556
    下载: 导出CSV

    表  4  不同冲击速度下蝴蝶形蜂窝夹芯板的横向位移

    Table  4.   Lateral displacement of the butterfly-shaped honeycomb sandwich panel at different impact velocities

    冲击速度/(m·s−1)中心最大横向位移/mm
    本文模型有限元模拟
    60.1770.190
    80.2470.252
    100.3200.311
    120.3950.374
    下载: 导出CSV

    表  5  矩形板和冲击器的材料参数和几何尺寸[26-27]

    Table  5.   Material parameters and geometrical sizes of the homogeneous panel and impactor[26-27]

    器件密度/(kg·m−3)弹性模量/GPa泊松比半径/mm长度/mm宽度/mm厚度/mm
    冲击器7971.82000.310
    矩形板7971.82000.32002008
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-01-17
  • 修回日期:  2023-05-30
  • 网络出版日期:  2023-05-30
  • 刊出日期:  2023-07-05

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