分数阶热弹理论下重力场对二维纤维增强介质的影响  

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

作　　者：段晓宇 马永斌[1] DUAN Xiaoyu;MA Yongbin(School of Science,Lanzhou University of Technology,Lanzhou 730050,P.R.China)

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《应用数学和力学》2021年第5期452-459,共8页Applied Mathematics and Mechanics

基　　金：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)。

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.Based on the fractional order generalized thermoelastic coupling theory proposed by Sherief et al,the thermoelastic problem of 2 D fiber-reinforced elastomers under thermal shock was studied.In view of the effects of gravity on 2 D 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.

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 

分 类 号：O343.6[理学—固体力学]