Abstract

In this paper, having or lacking a rotating, magnetic field, and a time-dependent source of heat on a two-dimensional homogeneous, isotropic, and thermoelastic half-space was illustrated. The governing equations were formulated in the considering Maxwell's stresses. The surface boundary settings were explored considering the thermoelasticity model of Green and Naghdi (type II). The techniques of the eigenvalue method and the normal mode analysis were utilized to resolve the non-dimensional coupled equations. We analyzed theoretically and computed numerically the rotation, time, wave number, frequency, and magnetic field. A comparison between having or lacking of the rotation was made with the results obtained. The displacement components, temperature, dilatation, and average of the normal stress were displayed in graphs to illustrate the physical meaning of the wavenumber, frequency, rotation, magnetic field, and time-dependent heat source. Normal stresses have been displayed graphically to show the physical meaning of the magnetic field, rotation, frequency, wave number, and time-dependent heat source. The results obtained show that having rotation, magnetic field, and time affects significantly eigenvalue issue, especially in astrophysics, aircraft, engineering, astronomy, petroleum extracting, and structures.

摘要

在本文中，说明了在二维均匀，各向同性和热弹性的半空间上是否具有旋转磁场，随时间变化的热源。在考虑麦克斯韦应力的情况下制定了控制方程。考虑了Green和Naghdi（II型）的热弹性模型，探讨了表面边界设置。利用特征值方法和法线模式分析技术来求解无量纲耦合方程。我们从理论上进行了分析，并通过数值计算了旋转，时间，波数，频率和磁场。将旋转的有无与获得的结果进行了比较。位移分量，温度，膨胀 图中显示了法向应力和平均应力的平均值，以说明波数，频率，旋转，磁场和随时间变化的热源的物理含义。正应力已以图形方式显示，以显示磁场，旋转，频率，波数和随时间变化的热源的物理含义。获得的结果表明，具有旋转，磁场和时间会显着影响本征值问题，尤其是在天体物理学，飞机，工程学，天文学，石油开采和结构中。