On the problem of radial vibrations in non-homogeneity isotropic cylinder under influence of initial stress and magnetic field

In the present work, the effects of initial stress, magnetic field and non-homogeneity on wave propagation of free harmonic waves in isotropic material are discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement and different cases of the boundary conditions for the hollow cylinder are considered. The determination is concerned with the eigenvalues of the natural frequencies of the radial vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, magnetic field and non-homogeneity.