Resumen de Radial vibrations on an elastic medium subjected to rotation and magnetic field
G.A. Yahya, Sherif El Bendary, A. M. Abd-Alla
Based on the one-dimensional elastic theory, the radial vibrations of cylindrical isotropic embedded in an elastic medium are studied in the paper. The effect of the magnetic field of the radial vibrations of an elastic hollow cylinder with rotation is researched as well. The one-dimensional equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free and fixed; the mixed boundary condition is numerically examined. The determination is concerned with the eigenvalues of the natural frequency of the radial vibrations in the case of harmonic vibrations. The effect of the magnetic field and rotation on the natural frequencies were explored. It was shown that the dispersion curves of guided waves were significantly influenced by the magnetic field and rotation of the elastic cylinder. Numerical results are given and graphically illustrated in each considered case. The natural frequencies and mode shapes are calculated numerically, and the effects of rotating, magnetic field, and variable thickness are discussed. It is observed that an increase of the magnetic parameter, as well as the rotation parameters, brings results closer to the classical cylinder theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage. The results indicate that the effects of the magnetic field and rotation are very pronounced.
