Nonlinear vibration behavior of a carry current ferromagnetic beam plate under magnetic fields and thermal loads

In order to study the magnetoelastic instability and natural frequency of a ferromagnetic plate under a magnetic field, different magnetic force models are considered. In the present study, considering more realistic assumptions, new equations for the study of the vibrational behavior of ferromagnetic beam plates carrying the electric current in the magnetic field are presented by employing the theory of Eringen and Maxwell relations. Conclusively, the effects of magnetic traction and thermal fields created by electric current and eddy currents are taken into account. The coupled nonlinear differential equations of the system are separated by the Galerkin method and solved numerically. The numerical results are compared with the results in the literature, and the effect of different parameters on the vibration characteristics of the soft ferromagnetic beam plate is investigated. The results show that the components of the force that are created by magnetic tractions, as well as the assumption of thermal couplings, can significantly change the vibrational behavior of the plates. Also, by increasing the intensity of the electric current and the magnetic field, the amplitude of the oscillations of the plate is increased and instability occurs for certain values of these parameters in the system.