石墨烯环氧树脂基复合材料梁屈曲前后的自由振动

张辉 宋敉淘

张辉, 宋敉淘. 石墨烯环氧树脂基复合材料梁屈曲前后的自由振动[J]. 高压物理学报, 2019, 33(5): 054102. doi: 10.11858/gywlxb.20190701
引用本文: 张辉, 宋敉淘. 石墨烯环氧树脂基复合材料梁屈曲前后的自由振动[J]. 高压物理学报, 2019, 33(5): 054102. doi: 10.11858/gywlxb.20190701
ZHANG Hui, SONG Mitao. Free Vibrations of Pre/Post-Buckled Graphene-Reinforced Epoxy Resin Matrix Nanocomposite Beams[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 054102. doi: 10.11858/gywlxb.20190701
Citation: ZHANG Hui, SONG Mitao. Free Vibrations of Pre/Post-Buckled Graphene-Reinforced Epoxy Resin Matrix Nanocomposite Beams[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 054102. doi: 10.11858/gywlxb.20190701

石墨烯环氧树脂基复合材料梁屈曲前后的自由振动

doi: 10.11858/gywlxb.20190701
基金项目: 国家自然科学基金(11302087);江苏省自然科学基金(BK20130479)
详细信息
    作者简介:

    张 辉(1991-),男,硕士研究生,主要从事结构动力学研究. E-mail:18605240606@163.com

    通讯作者:

    宋敉淘(1984-),男,博士,副教授,主要从事结构动力学研究. E-mail:songmt2004@163.com

  • 中图分类号: O343

Free Vibrations of Pre/Post-Buckled Graphene-Reinforced Epoxy Resin Matrix Nanocomposite Beams

  • 摘要: 采用微分求积法分析了石墨烯增强纳米复合材料梁屈曲前后的自由振动问题。考虑石墨烯纳米片在基体中随机排列和定向排列的情况,采用Halpin-Tsai微观力学模型估算两种模式下石墨烯纳米复合材料的弹性模量,并通过Hamilton原理建立基于一阶剪切变形理论下梁的动力学控制方程。利用微分求积法计算得到石墨烯纳米复合材料梁的临界屈曲载荷及屈曲前后的固有频率。数值计算结果表明:按合理排列模式掺杂较多的薄石墨烯纳米片,会大幅度提高梁的临界屈曲载荷以及屈曲前的固有频率;但屈曲发生后,同样的做法却会使结构的刚度降低。

     

  • 图  石墨烯纳米片在基体材料中的排列模式:(a)随机排列;(b)定向排列

    Figure  1.  Arrangement modes of graphene nanosheets in matrix materials: (a) random distribution; (b) orientation distribution

    图  不同条件下石墨烯纳米复合材料梁的临界屈曲荷载:(a)石墨烯纳米片的浓度不同;(b)石墨烯纳米片的长厚比不同;(c)梁的长细比不同

    Figure  2.  Critical buckling loads of graphene-reinforced nanocomposite beams under different conditions:(a) different concentrations of GPLs; (b) different aspect ratios of GPLs; (c) different length-to-thickness ratios of beams

    图  S-S约束下R-梁的前4阶临界屈曲模态

    Figure  3.  The first four-order critical buckling modes of R-beam under S-S boundary condition

    图  轴向力对不同模式梁第一阶固有频率的影响

    Figure  4.  Effect of axial force on the first-order natural frequency of beams with different GPL distribution modes

    图  轴向力对不同约束下梁固有频率的影响

    Figure  7.  Effect of axial force on the natural frequencies of beams with different boundary conditions

    图  轴向力对不同浓度下W-梁固有频率的影响

    Figure  5.  Effect of axial force on natural frequencies of W-beam with different graphene concentrations

    图  不同长厚比的GPLs对梁固有频率的影响

    Figure  6.  Effect of GPL length-to-thickness ratio on the natural frequencies of beams

    表  1  定向排列状态下片状增强纳米复合材料增强因子

    Table  1.   Enhancement factors of flake reinforced nanocomposites

    Material parameter${\zeta }$
    ${{G_{12}}}$${3{L_{\rm G}}/4{T_{\rm G}}}$
    ${{G_{13}}}$,${{G_{23}}}$${{L_{\rm G}}/{T_{\rm G}}}$
    下载: 导出CSV

    表  2  环氧树脂及石墨烯的材料参数

    Table  2.   Material parameters of epoxy resins and GPLs

    MaterialYoung’s modulus /GPaShear modulus /GPaDensity/(kg·m–3)Poisson’s ratio
    Epoxy resins[21]3.01.121200 0.34
    Graphene platelets[2223]1010280 1062.50.186
    下载: 导出CSV

    表  3  不同约束下石墨烯纳米复合材料梁的一阶屈曲荷载

    Table  3.   The first-order critical buckling load of graphene-reinforced nanocomposite beams with different boundary conditions

    Boundary conditionR-beamL-beamW-beam
    Euler beamThis work Euler beamThis work Euler beamThis work
    S-S 40.93 40.76 82.16 79.87 82.16 81.72
    C-C 163.71160.36328.65293.84328.65320.72
    C-S 83.53 82.98167.68158.00167.68166.23
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-01-03
  • 修回日期:  2019-01-23
  • 发布日期:  2019-07-25

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