分数阶热弹理论下二维纤维增强弹性体的动态响应问题

The Problem of Dynamic Response of Two Dimensional Fiber Reinforced Elastomer under Fractional Thermoelastic Theory

摘要: 本文内容基于Ezzat型分数阶广义热弹性耦合理论，研究半无限大空间模型下二维纤维增强弹性体受线性I型裂纹作用的热弹性问题。文中给出了分数阶广义热弹性理论下的控制方程，运用正则模态法对控制方程进行求解，得到了半空间无限大纤维增强弹性体中的无量纲应力、位移、温度等物理量的分布规律。重点研究了旋转效应及分数阶参数对各物理量的影响。研究结果表明：纤维增强弹性体在外载荷作用下出现了热弹耦合效应，分数阶参数以及旋转效应显著地影响了各物理量的分布规律。

Abstract: Based on the Ezzat type fractional generalized thermoelastic coupling theory, the thermoelastic problem of a two-dimensional fiber-reinforced elastic body subjected to a linear mode I crack in a semi infinite space is studied. In this paper, the governing equations under the fractional genera-lized thermoelastic theory are given, and the regularized modal method is used to solve the go-verning equations. The distribution of dimensionless temperature, displacement, stress and other physical quantities in the half space infinite fiber reinforced elastomer is obtained. The influence of fractional order parameters and rotation effect on the physical quantities is mainly studied. The results show that the thermoelastic coupling effect occurs in the fiber reinforced elastomer due to the external load, and the fractional order parameters and rotation effect significantly affect the distribution of physical quantities.