Magnetoelastic primary resonance of an axially moving ferromagnetic plate in an air gap field

Abstract

The air gap field widely exists in mechatronic systems to realize energy transfer, but the components in such systems are often regarded as rigid bodies. In this paper, elastomers in an air gap field are discussed for the first time. The magnetoelastic primary resonance of an axially moving ferromagnetic plate in an air gap field is investigated. With the magnetic wall armature as the electromagnetic source, the ferromagnetic thin plate moves axially parallel to the armature. An air gap field excited by the armature is distributed in thin air gap space between them. In addition to eddy current effects, the ferromagnetic thin plate in the air gap field will be magnetized to generate a harmonic magnetic force to excite the plate vibration, which results in the system existing nonlinear coupling characteristics between armature, plate deformation and air gap field. Considering the dynamic feedback of thin plate vibration on the air gap field by changing the air gap thickness, the magnetoelastic vibration equation of the plate is derived by the Hamilton's principle. The vibration differential equation for the simply supported plate is obtained via Galerkin method, and the static deflection of the plate under static magnetic load is solved. The multi-scale and Lyapunov methods are utilized to analyze the primary resonance under harmonic magnetic force, thus obtaining the steady-state resonance equation and the stability discriminants of stationary solutions. Through numerical simulations, the curves and three-dimensional surfaces of amplitude varying with different parameters are plotted. The variation of magnetic field strength, magnetic force, and electromagnetic torques under steady-state response is obtained. The results show that amplitude decreases with the increase of initial air gap thickness but increases with the increase of magnetic potential amplitude on the armature. Velocity has a suppression effect on system resonance, and there is an intrinsic coupling mechanism of action and reaction between the thin plate and air gap field.