The Effect of Rotation on the Free Vibrations in a Non-homogeneous Orthotropic Elastic Hollow Sphere

This article examines the radial vibrations of spherical isotropy embedded in an elastic medium according to the one-dimensional (1D) elastic theory. Based on the linear theory of elasticity, the rotation and inhomogeneity effects on wave propagation in orthotropic material are analyzed. The 1Delastodynamicsequation is solved in terms of radial displacement. We consider three boundaries: free, fixed, and mixed orthotropic materials. In the case of harmonic vibrations, the eigenvalues of the natural frequency of the radial vibrations for different boundary conditions are determined. For each case, the numerical results are presented, illustrated graphically, and then compared with those in the absence of rotation and non-homogeneity. An increase in the rotation and non-homogeneity parameters is observed, similar to the findings of the classical sphere theory. Therefore, this study can also be used in the design and optimization of microplates and nanoplates. The findings show that rotation and non-homogeneity have a strong impact on wave propagation in orthotropic material.