Magnetoelastic primary resonance and bifurcation of an axially moving ferromagnetic plate under harmonic magnetic force

Abstract

The magnetoelastic primary resonance and bifurcation of an axially moving ferromagnetic plate under harmonic magnetic force are investigated. In harmonic magnetic field, the ferromagnetic plate is subjected to harmonic magnetic force generated by magnetization. Based on the Hamilton principle, the nonlinear magnetoelastic transverse vibration equation of the plate under the combined action of mechanical load and harmonic magnetic force is derived. For simply supported boundary conditions, the discretized vibration differential equation is obtained by Galerkin method. The multi-scale method is used to solve the nonlinear primary resonance, and obtain the resonance characteristic equation under steady-state response. According to Lyapunov stability theory, the stability criterion of constant solutions is determined. Through numerical calculation, two-dimensional and three-dimensional characteristic diagrams of amplitude are plotted, and the parameter ranges corresponding to multivalued solution regions and stable solution regions are determined. Global bifurcation diagrams and maximum Lyapunov exponent spectrums are plotted for different control parameters, and the effects of control parameters on the dynamic response and stability of the system are analyzed. The results show that magnetic field strength, axial velocity and mechanical load have significant effects on the vibration characteristics of the system, and tiny variation of control parameters can lead to the dramatic change of system motion characteristics.