Forced Vibration Of Axially Moving Ferromagnetic Beam In Transverse Magnetic Field

With the continuous development of science and technology,axial motion system is widely used in engineering.Among them,nonlinear dynamics and stability problems caused by the axial movement of chord,beam and plate determine whether the overall structure is able to operate,especially under the multi-field such as force,electromagnetic,and temperature which producing more complex dynamic behavior.Therefore,it is necessary to deeply study the motion law of axial motion system.In this paper,the problem of magneto-elastic nonlinear forced vibration of axially moving ferromagnetic beam in a transverse magnetic field is studied.Based on theory of elastic mechanics,the expressions of potential energy and kinetic energy of axially moving ferromagnetic beam are given.From classical electromagnetic field theory,the expressions of electromagnetic force on the beam in magnetic field and magnetic force-couple are obtained.Based on the Hamiltonian variational principle,the magneto-elastic nonlinear vibration coupling equation of axially moving ferromagnetic beam is obtained.The magneto-elastic main resonance of axially moving ferromagnetic beams in a transverse magnetic field is studied.The magneto-elastic vibration equation of beam is Galerkin integral operation,and obtained vibration differential equation is dimensionless.Then multi-scale method is used to solve the magneto-elastic nonlinear coupled vibration differential equation,and the amplitude-frequency response equation of system is obtained.Through calculation examples,the amplitude-frequency curve,amplitude-external excitation force curve and amplitude-magnetic induction intensity curve are obtained.And analyzed under different parameter conditions.The problem of magneto-elastic primary resonance of an axially moving ferromagnetic beam with bidirectional excitation is studied.First,Galerkin integral and dimensionless processing are carried out on the magneto-elastic vibration equation of beam to obtain coupled vibration differential equation,thus amplitude-frequency response equation of system under different frequency coordination parameters is obtained.Through calculation examples,the amplitude-frequency curves of different materials ofdifferent frequency coordination parameters and the amplitude-external excitation force amplitude curves at different speeds are analyzed.Study the non-resonance problem of magneto-elastic nonlinearity of axially moving ferromagnetic beam in magnetic field.Multi-scale method is used to solve the vibration differential equations of system,and the nonlinear dynamic characteristics of system under strong excitation are analyzed.Through the obtained time-history diagram and phase diagram,the influence of excitation force,velocity and other parameters on nonlinear vibration characteristics of system is analyzed.