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纤维增强FGM梁的自由振动和临界屈曲载荷分析

滕兆春 王伟斌 马铃权

滕兆春,王伟斌,马铃权. 纤维增强FGM梁的自由振动和临界屈曲载荷分析[J]. 机械科学与技术,2022,41(12):1958-1964 doi: 10.13433/j.cnki.1003-8728.20200529
引用本文: 滕兆春,王伟斌,马铃权. 纤维增强FGM梁的自由振动和临界屈曲载荷分析[J]. 机械科学与技术,2022,41(12):1958-1964 doi: 10.13433/j.cnki.1003-8728.20200529
TENG Zhaochun, WANG Weibin, MA Lingquan. Analysis of Free Vibration and Critical Buckling Load of Fiber Reinforced FGM Beams[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(12): 1958-1964. doi: 10.13433/j.cnki.1003-8728.20200529
Citation: TENG Zhaochun, WANG Weibin, MA Lingquan. Analysis of Free Vibration and Critical Buckling Load of Fiber Reinforced FGM Beams[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(12): 1958-1964. doi: 10.13433/j.cnki.1003-8728.20200529

纤维增强FGM梁的自由振动和临界屈曲载荷分析

doi: 10.13433/j.cnki.1003-8728.20200529
基金项目: 国家自然科学基金项目(11662008)
详细信息
    作者简介:

    滕兆春(1969− ),副教授,研究方向为结构动力学和复合材料结构力学研究,tengzc@lut.edu.cn

  • 中图分类号: O343

Analysis of Free Vibration and Critical Buckling Load of Fiber Reinforced FGM Beams

  • 摘要: 基于经典梁理论(CBT)研究轴向力作用下纤维增强功能梯度材料(FGM)梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法(DTM)对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定(C-C)、固定-简支(C-S)和简支-简支(S-S)3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。
  • 图  1  纤维增强FGM梁的几何描述

    图  2  不同边界条件下刚度比$ {P_c}/{P_m} $对纤维增强FGM梁前5阶固有频率的影响

    图  3  不同边界条件下纤维体积分数Vf对纤维增强FGM梁前3阶无量纲固有频率的影响

    图  4  不同边界下刚度比$ {P_c}/{P_m} $对无量纲临界屈曲载荷的影响

    图  5  不同边界条件下纤维体积分数和无量纲临界屈曲载荷的关系曲线

    图  6  不同边界条件和不同纤维体积分数下无量纲压载荷对一阶无量纲固有频率的影响

    表  1  不同边界条件各向同性材料梁的无量纲固有频率

    边界Ω1Ω2Ω3Ω4Ω5
    C-C本文解22.373361.6728120.9034199.8588298.663
    文献[21]22.373361.6728120.903199.859298.556
    C-S本文解15.418249.9649104.2477178.2696274.1436
    文献[21]15.418249.9649104.248178.270272.031
    S-S本文解9.869639.478488.8264157.9136247.3156
    文献[21]9.869639.478488.8264157.914246.740
    下载: 导出CSV

    表  2  不同边界条件下FGM梁无量纲固有频率

    Pc/PmΩC-CC-SC-S
    本文解文献[21]本文解文献[21]本文解文献[21]
    Ω122.108022.10815.235415.2359.75269.7525
    2Ω260.941660.94249.372549.37339.011339.010
    Ω3119.4699119.47103.0117103.0187.773387.773
    Ω121.719721.72014.967814.9689.58139.5813
    3Ω259.871159.87148.505248.50538.325138.325
    Ω3117.3713117.37101.2022101.2086.231586.231
    Ω121.351821.35214.714314.7149.41909.4190
    4Ω258.857158.85747.683747.68437.67637.676
    Ω3115.3834115.3899.488299.48884.771084.771
    Ω121.019921.02014.485614.4869.27269.2726
    5Ω257.942457.94146.942746.94237.090537.090
    Ω3113.5903113.5997.942197.94283.453683.454
    下载: 导出CSV
  • [1] 张鹏. 纤维增强功能梯度材料梁静态力学行为分析[D]. 扬州: 扬州大学, 2012

    ZHANG P. Analysis of the static mechanical behavior of fiber-reinforced functionally graded material beams[D]. Yangzhou: Yangzhou University, 2012 (in Chinese)
    [2] 衡亚洲. 弹性地基上正交各向异性矩形板自由振动与屈曲的DTM求解[D]. 兰州: 兰州理工大学, 2017

    HENG Y Z. Free vibration and buckling analysis of orthotropic rectangular plates resting on elastic foundations by using DTM[D]. Lanzhou: Lanzhou University of Technology, 2017 (in Chinese)
    [3] REDDY J N, CHIN C D. Thermomechanical analysis of functionally graded cylinders and plates[J]. Journal of Thermal Stresses, 1998, 21(6): 593-626 doi: 10.1080/01495739808956165
    [4] WATTANASAKULPONG N, BUI T Q. Vibration analysis of third-order shear deformable FGM beams with elastic support by Chebyshev collocation method[J]. International Journal of Structural Stability and Dynamics, 2018, 18(5): 1850071 doi: 10.1142/S0219455418500712
    [5] EBRAHIMI F, GHADIRI M, SALARI E, et al. Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams[J]. Journal of Mechanical Science and Technology, 2015, 29(3): 1207-1215 doi: 10.1007/s12206-015-0234-7
    [6] GHAZARYAN D, BURLAYENKO V N, AVETISYAN A, et al. Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method[J]. Journal of Engineering Mathematics, 2018, 110(1): 97-121 doi: 10.1007/s10665-017-9937-3
    [7] BAGHLANI A, KHAYAT M, DEHGHAN S M. Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction[J]. Applied Mathematical Modelling, 2020, 78: 550-575 doi: 10.1016/j.apm.2019.10.023
    [8] 滕兆春, 昌博, 付小华. 弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解[J]. 中国机械工程, 2018, 29(10): 1147-1152 doi: 10.3969/j.issn.1004-132X.2018.10.003

    TENG Z C, CHANG B, FU X H. DTM analysis for free vibrations of rotating functionally graded material Timoshenko beams on elastic foundations[J]. China Mechanical Engineering, 2018, 29(10): 1147-1152 (in Chinese) doi: 10.3969/j.issn.1004-132X.2018.10.003
    [9] 林鹏程, 滕兆春. 热冲击下轴向运动FGM梁的自由振动分析[J]. 振动与冲击, 2020, 39(12): 249-256

    LIN P C, TENG Z C. Free vibration analysis of axially moving FGM beams under thermal shock[J]. Journal of Vibration and Shock, 2020, 39(12): 249-256 (in Chinese)
    [10] GUPTA A, TALHA M, SEEMANN W. Free vibration and flexural response of functionally graded plates resting on Winkler-Pasternak elastic foundations using nonpolynomial higher-order shear and normal deformation theory[J]. Mechanics of Advanced Materials and Structures, 2018, 25(6): 523-538 doi: 10.1080/15376494.2017.1285459
    [11] 蒋伟男, 郝育新, 吕梅. 几种边界条件下功能梯度夹层板自由振动分析[J]. 北京信息科技大学学报, 2020, 35(1): 15-22

    JIANG W N, HAO Y X, LYU M. Free vibration analysis of functional gradient sandwich plates under several boundary conditions[J]. Journal of Beijing Information Science & Technology University, 2020, 35(1): 15-22 (in Chinese)
    [12] 李万春, 滕兆春. 变曲率FGM拱的面内自由振动分析[J]. 振动与冲击, 2017, 36(9): 201-208

    LI W C, TENG Z C. In-plane free vibration analysis of FGM arches with variable curvature[J]. Journal of Vibration and Shock, 2017, 36(9): 201-208 (in Chinese)
    [13] 贺丹, 门亮. 碳纳米管增强型复合材料功能梯度板的自由振动模型与尺度效应[J]. 计算力学学报, 2018, 35(3): 326-330 doi: 10.7511/jslx20161028004

    HE D, MEN L. A free vibration model of carbon nanotube-reinforced functionally graded composite plates and scale effects[J]. Chinese Journal of Computational Mechanics, 2018, 35(3): 326-330 (in Chinese) doi: 10.7511/jslx20161028004
    [14] 李晓倩, 宋敉淘. 温度场下石墨烯增强功能梯度梁的主共振行为分析[J]. 河南科技大学学报(自然科学版), 2019, 40(1): 66-71

    LI X Q, SONG M T. Primary resonance of functionally graded graphene-reinforced nanocomposite beams in thermal environments[J]. Journal of Henan University of Science and Technology (Natural Science), 2019, 40(1): 66-71 (in Chinese)
    [15] NEJATI M, FARD K M, ESLAMPANAH A, et al. Free vibration analysis of reinforced composite functionally graded plates with steady state thermal conditions[J]. Latin American Journal of Solids and Structures, 2017, 14(5): 886-905 doi: 10.1590/1679-78253705
    [16] SHEN H S, XIANG Y. Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments[J]. Engineering Structures, 2013, 56: 698-708 doi: 10.1016/j.engstruct.2013.06.002
    [17] YAS M H, SAMADI N. Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation[J]. International Journal of Pressure Vessels and Piping, 2012, 98: 119-128 doi: 10.1016/j.ijpvp.2012.07.012
    [18] THOMAS B, INAMDAR P, ROY T, et al. Finite element modeling and free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotubes[J]. International Journal on Theoretical and Applied Research in Mechanical Engineering, 2013, 2(4): 97-102
    [19] DING K, WENG G J. The influence of moduli slope of a linearly graded matrix on the bulk moduli of some particle- and fiber-reinforced composites[J]. Journal of Elasticity, 1999, 53(1): 1-22
    [20] CLYNE T W, HULL D. An Introduction to Composite Materials[M]. 3rd ed. New York: Cambridge University Press, 2019
    [21] BOUAMAMA M, ELMEICHE A, ELHENNANI A, et al. Exact solution for free vibration analysis of FGM beams[J]. Revue des Composites et des Matériaux Avancés-Journal of Composite and Advanced Materials, 2020, 30(2): 55-60
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出版历程
  • 收稿日期:  2020-12-08
  • 网络出版日期:  2023-02-18
  • 刊出日期:  2022-12-05

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