Abstract: Based on the expressions of kinetic energy, strain energy and virtual work done by electromagnetic forces, the nonlinear magneto-elastic vibration equations of an axially moving strip thin plate in transverse magnetic field are deduced by using Hamilton principle. Based on displacement mode hypothesis, by using Galerkin method, vibration differential equations in the form of three orders displacement mode of axially moving thin plate with two simply supported are obtained. Principal resonance problem solved by using multiple scales method and amplitude-frequency response functions of steady solution in three different frequency relationships are obtained. Based on Liaypunov theory, stability of solution is analyzed and the critical condition of stability is determined. By the numerical examples, variation of amplitude curves in the cases of different axially moving velocity, magnetic induction intensity and thick of thin plate are obtained. The influence of different parameters on resonance amplitude and nonlinear characteristics are analyzed and different frequency relationship is compared.

Key words: Axially moving, Hamilton principle, Magneto-elastic, Principal resonance, Stability