Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder

The present paper investigates the frequencies based on the radial vibrations of a non-homogeneous elastic cylinder using different boundary conditions (BCs) under the rotating, non-homogeneity, and magnetic field effects. Three different BCs, the free, mixed, and fixed, are implemented. The solution is related to using the eigenvalues based on the radial vibrations frequencies for different boundary conditions in harmonic vibrations. The numeric outcomes are demonstrated graphically for each case-the comparison of the results in the nonappearance and variation of the non-homogeneity, rotating effects, and magnetic field. The obtained outcomes specify the rotating, non-homogeneity, and magnetic field effects.