Effects of the Gravity Field on 2D Fiber-Reinforced Media Under the Fractional Order Theory of Thermoelasticity
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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.
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关键词:
- 二维模型 /
- 正则模态法 /
- 重力场 /
- 分数阶广义热弹性理论 /
- 热冲击
Abstract: Based on the fractional order generalized thermoelastic coupling theory proposed by Sherief et al, the thermoelastic problem of 2D fiber-reinforced elastomers under thermal shock was studied. In view of the effects of gravity on 2D fiber-reinforced linearly thermoelastic isotropic media, the governing equations were established. Through the normal mode analysis and numerical calculation, the governing equations were solved, and the expressions of the dimensionless temperature, the displacement components and the stress under different fractional order parameters and different gravity fields were obtained. The distributions of variables were illustrated and the results were discussed. The results show that, the gravity field and fractional order parameters have significant impacts on the displacements and stresses of the fiber-reinforced media, but the influence on the temperature is limited. -
[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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