Natural Vibration Of Axially Moving Ferromagnetic Beams In Magnetic Field

Nonlinear and multi-field coupled vibration of beam,plate and chord structures has been a hot research topic.The conclusions obtained by calculation can provide theoretical reference for practical problems encountered in engineering.With the establishment of electromagnetic structure model,a more comprehensive research framework for structural vibration in magnetic field environment has been established.Therefore,more and more scholars begin to study the magnetoelastic vibration of structures.In this paper,the magnetoelastic natural vibration of a ferromagnetic beam moving axially in a constant magnetic field is studied.According to the basic theory of elasticity,the expressions of kinetic energy and potential energy of axially moving ferromagnetic beams are given.According to the basic theory of electromagnetic field,the basic expressions of electromagnetic force considering perturbation magnetic field are given.Then,the nonlinear magnetoelastic bi-directional coupled vibration equation of axially moving ferromagnetic beams in magnetic field is obtained by using Hamiltonian variational principle.The model of an axially moving ferromagnetic beam with hinged boundary in a constant magnetic field is studied.The time and space variables are separated by Galerkin method,and the magnetoelastic bi-directional vibration differential equation of the beam is obtained.The linear natural vibration of beams is studied by neglecting the small influence of the non-linear term on the vibration of beams.According to the theory of vibration,the expression of natural frequency of beam under two-way vibration is given.The two-way natural frequencies and damping ratios of ferromagnetic beams are plotted through an example.The effects of axial velocity,magnetic induction intensity and different materials on the natural vibration of the system are analyzed.The problem of nonlinear natural vibration of axially moving ferromagnetic beams in a constant magnetic field is studied.The Galerkin method is used to obtain the non-linear differential equation of the two-way coupling vibration of the beam,and the multi-scale method is used to solve the natural frequency expression of the beam in the two-way coupling vibration.The curves of natural frequencies of two-way vibration of beams are plotted by maltab.The variation of natural frequencies of beams with time,axial velocity,magnetic induction intensity and different materials are analyzed.The internal resonance of axially moving ferromagnetic beams in a constant magnetic field is studied.The multi-scale method is used to solve the characteristic equation of the coupling of beams when internal resonance occurs.The time history response diagram of the resonance amplitude of the system is obtained through an example.The influence of the magnetic induction intensity and the axial velocity on the resonance characteristics of the system is analyzed.