The Effect of Aerodynamic Loads on Nonlinear Vibration Behavior of a Ferromagnetic Beam-Plate under Magnetic Fields*

In order to study the mechanical behavior of a ferromagnetic rectangular thin beam-plate under the magnetic field and aerodynamic load, the electrodynamic equation are derived based on the Maxwell equations and the electromagnetic constitutive relations. The basic set of equations for nonlinear electromagnetic elasticity vibration expressed by the displacement of a thin beam-plate in a transverse magnetic field is obtained. In addition, we study the nonlinear principal resonance and the solution stability of a thin plate with two opposite sides simply supported and subjected to an aerodynamic pressure in a constant transverse magnetic field. The coupled nonlinear differential equations of the system, are discarded by Galerkin method and solved numerically to characterize the phenomena of magnetoelastic buckling and instability of the plates. Then the effect of different parameters on the vibration characteristics of the soft ferromagnetic beam-plate and the effects of magnetic tractions and thermal fields which created by plate vibration is investigated