Electromagnetic Effect On Natural Vibration Of Axially Moving Ferromagnetic Rectangular Plate

Due to the breakthrough development of the research on engineering and technology,ferromagnetic structures have gained a wide prospect of application in daily life and industrial fields such as aerospace and automotive.Ferromagnetic materials,due to good magnetization and magnetic energy conversion characteristics,can lead to more complex dynamics behaviors for the system when operating in multiple coupling fields including such as force,magneto,elastic and motion.In addition,the ferromagnetic structure in a magnetic field is significantly influenced by electromagnetic and magnetization effects.Therefore,it is important to study the magnetoelastic vibration of axially moving ferromagnetic thin plates under the magnetization effect and motion effect.Based on the elastic bending theory,the expressions of kinetic energy and potential energy for the axially moving rectangular plate are derived.The expressions of magnetization force are obtained by the basic electromagnetic theory and the magneto-solid coupling theory.The principle is used to derive the nonlinear magneto-elastic vibration equations of the axially moving ferromagnetic rectangular plate in the magnetic field environment.The nonlinear natural vibration of the axially moving rectangular plate under the action of a constant magnetic field is studied.For rectangular thin plates with two boundary constraints: simply supported on four sides and simply supported on opposite sides,clamped on opposite sides,the disturbance differential equations of systems under the action of static magnetic force are derived via the Galerkin method.Moreover,the first-order and secondorder analytical equations of the natural frequencies for the axially moving rectangular plate in a constant magnetic field are obtained by the multi-scale method.Through numerical calculations,the curves of the intrinsic frequencies varying with the axial velocity,magnetic field strength,and initial amplitude under the two boundary conditions are presented,respectively.The effect of different physical and geometric parameters on the dynamics characteristics of the multi-field coupling system is analyzed.The nonlinear natural vibration of an axially moving rectangular plate in the air-gap magnetic field is studied.The mechanical model of the axially moving ferromagnetic rectangular plate in the air-gap magnetic field environment is established.The distribution of air-gap magnetic field was determined by solving the magnetic potential equation in the air-gap space.For rectangular thin plates with two boundary constraints simply supported on four sides and simply supported on opposite sides,clamped on opposite sides,the Galerkin method and multi-scale method are employed to obtain the expressions of first two order natural frequencies for the axially moving rectangular plate in the air-gap magnetic field.Through numerical calculations,the curves of natural frequencies varying with the axial velocity,magnetic potential,air gap thickness and initial amplitude are plotted,and the results of the two analytical methods are compared and analyzed.The multi-order linear natural vibration of axially moving rectangular thin plates in an air-gap magnetic field was studied.Based on the magnetoelastic vibration equations of thin plates,the Galerkin method is applied for the discretization of a solution to obtain the natural vibration characteristic equations under three boundary constraints simply supported on four sides,clamped at four sides and simply supported on opposite sides,clamped on opposite sides.Through numerical calculations,the curves of the multi-order natural frequencies for a thin plate in an air-gap magnetic field varying with axial velocity,magnetic potential,airgap thickness are presented.The effect of different boundary constraints on the vibration characteristics is analyzed,and the analytical and numerical solutions are compared for verification.