Dual-mode coupling resonance and dynamic stability of axially moving ferromagnetic thin plate strips in alternating magnetic field

Abstract

This paper investigates the dual-mode coupling resonance and dynamic stability of axially moving ferromagnetic thin plate strips in alternating magnetic field. According to the basic electromagnetic theory and the magnetoelastic mechanics model, Lorentz electromagnetic force and torque generated by eddy current effect and the magnetizing force generated by magnetization are determined for the ferromagnetic plate strip. Introducing Von Karman geometric nonlinearity, the nonlinear governing equation of axially moving ferromagnetic plate strips under the combined action of mechanical load and magnetizing force is established by Hamilton's principle. For the simply supported plate strip, Galerkin method and the multi-scale method are employed to solve the modal coupling resonance dominated by electromagnetic excitation, obtaining the amplitude-frequency response equations. The stability of resonance responses is analyzed by the Lyapunov stability theory. Through parametric research, the amplitude-frequency characteristic curves, bifurcation diagrams and Lyapunov exponent spectra of each mode are plotted; the effect of different parameters on vibration characteristics and dynamic stability under the modal coupling is analyzed for the system. The results show that as one of the modal amplitudes enters the resonance region, the other modal amplitude decays into the "collapse" region due to energy exchange between modes; each modal amplitudes has more complex multi-valued and jumping phenomena for the nonlinear coupling effect. The increase in velocity will affect the stability of system; the enhancement of magnetic field will make the system change into chaos at high velocity.