Abstract

In this work, the fractional order theory of thermoelasticity is introduced to study a two-dimensional fiber-reinforced problem in a half-space. The governing equations are formulated by considering the effect of the magnetic field, gravity, and moving heat source on a fiber-reinforced linearly thermoelastic isotropic medium. These equations are then transformed into non-dimensional forms. The normal mode analysis is used to solve this problem to obtain the exact expressions of the non-dimensional temperature, displacement components, and stress. The distributions of these considered variables are obtained and illustrated graphically. Comparisons are taken with the results in the presence and absence of the magnetic field, gravity and heat source under the fractional order theory of thermoelasticity. The results show that the existence of the magnetic field, gravity, and heat source have significant influence on the distributions of the considered variables.

摘要

在这项工作中，引入了热弹性分数阶理论，以研究半空间中的二维纤维增强问题。通过考虑磁场，重力和移动热源对纤维增强的线性热弹性各向同性介质的影响来制定控制方程。然后将这些方程式转换为无量纲形式。使用正常模式分析来解决此问题，以获得无量纲温度，位移分量和应力的精确表达式。这些考虑的变量的分布已获得并以图形方式说明。根据热弹性分数阶理论，对存在和不存在磁场，重力和热源的结果进行比较。