Magneto-thermoelastic free vibration and traveling wave stability of a rotating ferromagnetic functionally graded cylindrical shell

The free vibration and traveling wave stability of a rotating ferromagnetic functionally graded cylindrical shell in magnetic and temperature fields are explored. The geometric and physical equations are determined within the framework of the Love's theory. The expressions of kinetic energy and strain energy are obtained by considering temperature and rotation effects. The magnetoelastic theory is employed to establish a model of magnetic force. By using Hamilton's principle and Galerkin truncation, the governing equations are obtained. The effects of different parameters on the natural frequencies of forward and backward waves are determined. It is found that the natural frequency undergoes separation of forward and backward waves due to the Coriolis force; with increase in the circumferential wave number, the frequency shows a trend of first decreasing and then increasing. The coupling effect of the magnetic induction intensity, rotational speed, power-law index, and thickness-to-diameter ratio leads to the nonlinear trend of frequencies. In addition, the influence of different parameter variations on the traveling wave stability is discussed.