Abstract

In this work, a mathematical system of wave propagation in generalized thermo-piezoelectric anisotropic smart material under primary magnetic field and rotation influence is considered. The system of equations for this phenomenon are given in the case of generalized thermoelasticity for three models, namely, Lord–Shulman (LS), Green–Lindsay (GL), and dual-phase-lag (DPL). Furthermore, it is assumed the whole medium is revolved with a regular angular velocity and perturbed magnetic field. Next, the normal mode technique is given to the set of partial differential equations to produce the corresponding ordinary differential equations whose exact analytical solutions will be found. The distributions of the considered variables such as the horizontal and vertical displacements, the temperature, the stress components, the electric potential, and the electric displacement are calculated numerically. Finally, the impacts of the rotation, primary magnetic field, and thermal relaxation times have been illustrated graphically which were noticeable on the various physical quantities.

摘要

在这项工作中，考虑了在初级磁场和旋转影响下广义热压电各向异性智能材料中波传播的数学系统。该现象的方程组在广义热弹性的情况下给出了三个模型，即 Lord-Shulman (LS)、Green-Lindsay (GL) 和双相滞后 (DPL)。此外，假设整个介质以规则的角速度和扰动的磁场旋转。接下来，对偏微分方程组采用正态模式技术，以生成相应的常微分方程，其精确解析解将被找到。所考虑变量的分布，例如水平和垂直位移、温度、应力分量、电势、并以数值方式计算电位移。最后，旋转、主磁场和热弛豫时间的影响已用图形说明，这些影响在各种物理量上都很明显。