Abstract

This article examines the free vibrations of spherical orthotropic within an elastic medium according to the one-dimensional (1D) elastic model. According to the linear elasticity model, rotation, magnetic field, and inhomogeneity effects on wave propagation in the orthotropic material are analyzed. The 1D magneto-elastodynamics equation is resolved concerning radial displacement. We consider three boundaries: free, fixed, and mixed orthotropic materials. Concerning harmonic vibrations, the eigenvalues of the natural frequency of the radial vibrations concerning various boundary settings are determined. For each case, the numerical results are provided, illustrated in graphs, and compared with those without rotation, magnetic field, and non-homogeneity. An increase in the rotation and non-homogeneity parameters is observed, similar to the findings of the classical sphere theory. The findings show that rotation, magnetic field, and non-homogeneity have a strong impact on wave propagation in orthotropic material. Increasing the rotation, magnetic field, and inhomogeneity parameters make the findings closer to the findings of the classical sphere model. Moreover, the present article applies to the design and optimal use of nanoplates and microplates. The findings show that the impacts of the magnetic field, rotation, and inhomogeneity parameter are very pronounced.

摘要

本文根据一维 (1D) 弹性模型研究弹性介质内球形正交各向异性的自由振动。根据线性弹性模型，分析了正交各向异性材料中的旋转、磁场和不均匀性对波传播的影响。一维磁弹性动力学方程解决了关于径向位移的问题。我们考虑三个边界：自由、固定和混合正交各向异性材料。关于谐波振动，确定了涉及各种边界设置的径向振动的固有频率的特征值。对于每种情况，都提供了数值结果，用图表说明，并与没有旋转、磁场和非均匀性的结果进行比较。观察到旋转和非均匀性参数的增加，类似于经典球体理论的发现。研究结果表明，旋转、磁场和非均匀性对正交各向异性材料中的波传播有很大影响。增加旋转、磁场和不均匀性参数使研究结果更接近经典球体模型的研究结果。此外，本文适用于纳米板和微板的设计和优化使用。研究结果表明，磁场、旋转和不均匀性参数的影响非常明显。此外，本文适用于纳米板和微板的设计和优化使用。研究结果表明，磁场、旋转和不均匀性参数的影响非常明显。此外，本文适用于纳米板和微板的设计和优化使用。研究结果表明，磁场、旋转和不均匀性参数的影响非常明显。