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分数阶热弹理论下重力场对二维纤维增强介质的影响

段晓宇 马永斌

段晓宇, 马永斌. 分数阶热弹理论下重力场对二维纤维增强介质的影响[J]. 应用数学和力学, 2021, 42(5): 452-459. doi: 10.21656/1000-0887.410125
引用本文: 段晓宇, 马永斌. 分数阶热弹理论下重力场对二维纤维增强介质的影响[J]. 应用数学和力学, 2021, 42(5): 452-459. doi: 10.21656/1000-0887.410125
DUAN Xiaoyu, MA Yongbin. Effects of the Gravity Field on 2D Fiber-Reinforced Media Under the Fractional Order Theory of Thermoelasticity[J]. Applied Mathematics and Mechanics, 2021, 42(5): 452-459. doi: 10.21656/1000-0887.410125
Citation: DUAN Xiaoyu, MA Yongbin. Effects of the Gravity Field on 2D Fiber-Reinforced Media Under the Fractional Order Theory of Thermoelasticity[J]. Applied Mathematics and Mechanics, 2021, 42(5): 452-459. doi: 10.21656/1000-0887.410125

分数阶热弹理论下重力场对二维纤维增强介质的影响

doi: 10.21656/1000-0887.410125
基金项目: 国家自然科学基金(地区科学基金)(12062011);国家自然科学基金(面上项目)(11972176)
详细信息
    作者简介:

    段晓宇 (1996—),女,硕士(E-mail: 437654495@qq.com);马永斌 (1974—),男,副教授,博士,硕士生导师(通讯作者. E-mail: myb_ssy@lut.cn).

  • 中图分类号: O343.6

Effects of the Gravity Field on 2D Fiber-Reinforced Media Under the Fractional Order Theory of Thermoelasticity

Funds: The National Natural Science Foundation of China(11972176)
  • 摘要: 基于Sherief等提出的分数阶广义热弹性耦合理论,研究了在热冲击作用下二维纤维增强弹性体的热弹性问题.考虑了重力对二维纤维增强线性热弹性各向同性介质的影响,建立了控制方程.运用正则模态法,经过数值计算,对控制方程进行求解,得到了不同分数阶参数和不同重力场下无量纲温度、位移和应力分量的表达式,以图形的方式展示了变量的分布规律并对结果展开了讨论.研究结果为:重力场和分数阶参数对纤维增强介质的位移及应力有着重要的影响,但对温度的影响有限.
  • [1] LORD H W, SHULMAN Y A. A generalized dynamical theory of thermoelasticity[J]. Journal of the Mechanics and Physics of Solids, 1967,15(5): 299-309.
    [2] GREEN A E, LINDSAY K A. Thermoelasticity[J]. Journal of Elasticity, 1972,2(1): 1-7.
    [3] GREEN A E, NAGHDI P M. On undamped heat waves in an elastic solid[J]. Journal of Thermal Stresses, 1992,15(2): 252-264.
    [4] POVSTENKO Y Z. Fractional heat conduction equation and associated thermal stress[J]. Journal of Thermal Stresses, 2004,28(1): 83-102.
    [5] POVSTENKO Y Z. Fundamental solutions to central symmetric problems for fractional heat conduction equation and associated thermal stresses[J]. Journal of Thermal Stresses,2008,31(1): 127-148.
    [6] SHERIEF H H, EL-SAYED A M A, EL-LATIEF A M. Fractional order theory of thermoelasticity[J]. International Journal of Solids and Structures,2010,47(2): 269-275.
    [7] SHERIEF H H, EL-LATIEF A M. Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity[J]. International Journal of Mechanical Sciences,2013,74(13): 185-189.
    [8] EZZAT M A, EL-KARAMANY A S. Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures[J]. Zeitschrift fur Angewandte Mathematik und Physik,2011,62(5): 937-952.
    [9] EZZAT M A, FAYIK M A. Fractional order theory of thermoelastic diffusion[J]. Journal of Thermal Stresses,2011,34(8): 851-872.
    [10] YOUSSEF H M. Two-dimensional thermal shock problem of fractional order generalized thermoelasticity[J]. Acta Mechanica,2012,223(6): 1219-1231.
    [11] YOUSSEF H M, AL-LEHAIBI E A. Fractional order generalized thermoelastic half-space subjected to ramp-type heating[J]. Mechanics Research Communications,2010,37(5): 448-452.
    [12] MA Yongbin, LIU Zequan, HE Tianhu. Two-dimensional electromagneto-thermoelastic coupled problem under fractional order theory of thermoelasticity[J].Journal of Thermal Stresses,2018,〖STHZ〗 41(5): 645-657.
    [13] MA Yongbin, LIU Zequan, HE Tianhu. A two-dimensional fibre-reinforced mode-Ⅰ crack problem under fractional order theory of thermoelasticity[J]. Mechanics of Composite Materials and Structures,2020,27(1): 34-42.
    [14] MA Yongbin, PENG Wei. Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity[J]. Journal of Thermal Stresses,2018,41(3): 302-312.
    [15] 马永斌, 何天虎. 基于分数阶热弹性理论的含有球型空腔无限大体的热冲击动态响应[J]. 工程力学, 2016,〖STHZ〗 33(7): 31-38.(MA Yongbin, HE Tianhu. Thermal shock dynamic response of an infinite body with a spherical cavity under fractional order theory of thermoelasticity[J]. Engineering Mechanics, 2016,33(7): 31-38.(in Chinese))
    [16] MA Y B, CAO L C, HE T H. Variable properties thermopiezoelectric problem under fractional thermoelasticity[J]. Smart Structures and Systems,2018,21(2): 163-170.
    [17] SINGH B. Wave propagation in thermally conducting linear fibre-reinforced composite materials[J]. Archive of Applied Mechanics,2006,75(8/9): 513-520.
    [18] OTHMAN M I, SAID S M, SARKER N. Effect of hydrostatic initial stress on a fiber-reinforced thermoelastic medium with fractional derivative heat transfer[J]. Multidiscipline Modeling in Materials and Structures,2013,9(3): 410-422.
    [19] BROMWICH T J I’A. On the influence of gravity on elastic waves, and, in particular on the vibrations of an elastic globe[J]. Proceedings of the London Mathematical Society,1898,30(1): 98-120.
    [20] 艾拉瓦利亚·P, 纳拉·N·S. 在重力作用下的上覆无限热弹性流体对广义热弹性固体转动的影响[J]. 应用数学和力学, 2009,30(12): 1415-1426.(AILAWALIA P, NARAH N S. Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid[J]. Applied Mathematics and Mechanics,2009,30(12): 1415-1426.(in Chinese))
    [21] OTHMAN M I A, SAID S M. Effect of gravity field and moving internal heat source on a 2-D problem of thermoelastic fiber-reinforced medium: comparison of different theories[J]. Mechanics of Advanced Materials and Structures,2019,26(9): 796-804.
    [22] BELFIELD A J, ROGERS T G, SPENCER A J M. Stress in elastic plates reinforced by fibres lying in concentric circles[J]. Journal of the Mechanics and Physics of Solids,1983,31(1): 25-54.
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出版历程
  • 收稿日期:  2020-05-06
  • 修回日期:  2020-10-16
  • 刊出日期:  2021-05-01

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