Abstract

This article is carried out with the Green-Naghdi theory of thermoelasticity with memory-dependent derivative to study the effects of a magnetic field and laser pulse in a generalized thermoelastic orthotropic elastic medium. Utilizing Laplace and Fourier integral transform to solve the problem analytically, the fundamental equations of the two-dimensional problem are expressed as a vector-matrix differential form, which is then solved by the eigen function expansion method. A numerical technique is utilized for the inversion process of Fourier and Laplace transforms. For different kernel functions, time delay, the effect of the magnetic field, and laser pulse, the variations of the stress distributions, displacement, and temperature are expressed graphically. The consequences of the current model are compared with the existing thermoelastic models. Significant capability is demonstrated due to the presence of the magnetic field, laser pulse, as well as memory-dependent derivative.

摘要

本文利用Green-Naghdi热弹性理论与记忆相关导数研究磁场和激光脉冲在广义热弹性正交各向异性弹性介质中的影响。利用拉普拉斯和傅里叶积分变换对问题进行解析求解，将二维问题的基本方程表示为向量-矩阵微分形式，然后通过特征函数展开法求解。数值技术用于傅里叶和拉普拉斯变换的反演过程。对于不同的核函数、时间延迟、磁场和激光脉冲的影响，应力分布、位移和温度的变化以图形方式表示。当前模型的结果与现有的热弹性模型进行了比较。由于存在磁场、激光脉冲以及依赖于记忆的导数，因此证明了显着的能力。