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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.

The effect of rotation on the free vibrations in a non-homogeneous orthotropic magneto-elastic hollow sphere