Chaos prediction and bifurcation of soft ferromagnetic thin plates with motion in dual air-gap magnetic fields excited by armatures

In this paper, chaotic prediction and bifurcation analysis are carried out for axially moving soft ferromagnetic thin plates in dual side air-gap magnetic fields. The two wall armatures and the moving ferromagnetic plate placed parallel between them form dual side air-gap regions for physical separation. For the non-current-carrying air-gap regions, according to Maxwell's equations and magnetic potential boundary conditions under vibration-displacement influence, the air-gap magnetic field distribution is determined by solving the magnetic potential boundary value problem. Based on the magnetoelastic mechanics model of ferromagnets and considering harmonic armature magnetic potentials, the magnetizing excitation of the ferromagnetic plate due to its magnetization in dynamic air-gap magnetic fields is given. Under magnetizing excitation, the system is mediated by air-gap magnetic fields to produce complex magnetoelastic coupling behavior through the spatial join between air-gap regions and the vibrationally deformed thin plate. The nonlinear magnetoelastic equation of motion for the system is derived by Hamilton's principle. The modal equation is obtained by spatio-temporal separation using the Galerkin method. Through the pitchfork bifurcation conditions, the parameter ranges for which Melnikov method is applicable are obtained, and then, the critical necessary condition and parameter domains for the occurrence of horseshoe chaos are determined. The basins of attraction are plotted using the cell mapping method to analyze the effect of magnetic potential amplitude on global characters of the system. In addition, the validity of chaotic parameter domains predicted by Melnikov method is verified by comparing with the chaotic bands and regions obtained by numerical method. The bifurcation diagrams and maximum Lyapunov exponential spectrums under axial velocity, amplitude of magnetic potential and its frequency as bifurcation parameters are plotted to illustrate the evolution of system into chaos and the dynamic stability.