The primary purpose of this paper is to examine the role of initial stress, magnetic field, coefficient of heat transfer, and inhomogeneity coefficients on the Rayleigh wave propagation. A liquid medium with an inhomogeneity coefficient associated with the density in the form of a trigonometric and linear function of depth has been considered. It is laid over an orthotropic rotating magneto-thermo-elastic medium under gravity and initial stress. By employing suitable mathematical treatment, displacements have been found in the form of $Mathieu$ and $Airy$ functions. The frequency equation has been achieved analytically with the help of natural boundary conditions. Numerical calculations and discussions have been performed with the help of graphical presentation, justifying the impact of inhomogeneity coefficients. As an outcome, a significant effect of initial stress and magnetic field on Rayleigh wave propagation has also been observed, which finds its application towards geophysical prospecting, wave mechanics, civil engineering, and mechanical engineering.

本文的主要目的是研究初始应力、磁场、传热系数和不均匀系数对瑞利波传播的作用。考虑了一种液体介质，其不均匀系数与密度相关，呈深度的三角函数和线性函数的形式。它位于重力和初始应力作用下的正交各向异性旋转磁热弹性介质上。通过采用适当的数学处理，发现位移的形式为$米A吨H我\mathrm{电子}你$和$A我r是$功能。在自然边界条件的帮助下，频率方程已通过解析获得。在图形表示的帮助下进行了数值计算和讨论，证明了不均匀系数的影响。结果，还观察到了初始应力和磁场对瑞利波传播的显着影响，这在地球物理勘探、波浪力学、土木工程和机械工程中得到了应用。