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Based on Hamilton principle, the nonlinear magneto-elastic vibration equation of ferromagnetic plate is established under the combined action of mechanical load and harmonic magnetic force induced by magnetization. For the boundary conditions with two long simply supported edges, the transverse vibration differential equations after variables separation is obtained by Galerkin method. The multi-scale method and Lyapunov stability theory are used to solve the first-order principal resonance problem under electromagnetic excitation, the amplitude-frequency equation and the stability criterion of the steady-state solutions are obtained. Through numerical examples, the amplitude-frequency characteristic curves, the amplitude-magnetic field intensity curves and the amplitude-velocity variation curves of the ferromagnetic plate are obtained. The results show that the amplitude of stable solutions increases with the increase of magnetic field intensity amplitude. The nonlinear stiffness increases with the increase of the velocity, the hard-spring characteristics are enhanced and the nonlinear characteristics are more significant.