Vibration and dynamic instability of ferromagnetic thin plates in magnetic fields

In this study, the vibration equation of a ferromagnetic thin plate in a magnetic field is derived by using Hamilton's principle under the assumptions of small vibration amplitude and quasistatic field. It is shown that the frequency of a ferromagnetic plate in a transverse field decreases with the field increase and the frequency of the plate in a longitudinal field increases with the field. Further, the principal instability regions in a transverse and a longitudinal field are given.