Dynamic Stability of Ferromagnetic Beam-Plates with Magnetoelastic Interaction and Magnetic Damping in Transverse Magnetic Fields

The dynamic stability of a soft ferromagnetic beam-plate in a transverse magnetic field is investigated. The fundamental equations of the ferromagnetic beam-plate including magnetoelastic interaction and magnetic damping are derived. Based on a magnetoelastic linearized method and perturbation technique, an expression for magnetoelastic stability of the ferromagnetic beam-plate system including magnetization and magnetic damping is explicitly obtained. In the analysis, the actual magnetic field coupled with the deformed ferromagnetic beam-plate is divided into a rigid magnetic field for the undeformed plate and a disturbed field for the deformed plate due to small displacement. It is shown that there exists two stable states involving magnetic damping stable oscillation and overdamping asymptotically stable motion, before the beam-plate loses its stability by static divergence. The effect of magnetic and geometrical parameters of the ferromagnetic beam-plate on critical magnetic field is discussed in detail.