Dynamic stability of ferromagnetic plate under transverse magnetic field and in-plane periodic compression

The dynamic stability of a soft ferromagnetic rectangular and simply supported plate immersed in an applied transverse magnetic field, as well as subjected to an in-plane periodic compression is presented in this paper. The fundamental equations involving magnetoelastic interaction and magnetic damping effect for the ferromagnetic plate are developed. In the theoretical model, the expression of induced magnetic force is based on a generalized magnetoelastic variational model, and the magnetic damping is due to the Lorentz body force arising from eddy current in the ferromagnetic material. By means of a linearized magnetoelastic theory and perturbation technique, the motion equation of the ferromagnetic plate is reduced to a damped Mathieu's equation and solved. The dynamic stability of the magnetoelastic system without in-plane compression is theoretically analyzed first, to show that there exist two stable states: magnetic damped stable oscillation, and over-damped asymptotically stable motion before static divergence instability of the ferromagnetic plate occurs. The dynamic instability and stability regions for the parametric excitation of the ferromagnetic plate due to the harmonically excited in-plane compression are obtained next. The effects of magnetic damping and excitation frequency of the in-plane periodic compression on the stability regions are discussed in detail.