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

In the present paper, the effect of the rotation and non-homogeneous on the free vibrations in an orthotropic material is studied. The fundamental equation of elastodynamic is solved in terms of radial displacement. The boundary conditions are considered, namely the free, fixed and mixed. The determination is concerned with the natural frequency of the free vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically in each case considered. Comparisons are made with the results in the absence of rotation and non-homogeneity.