Magnetoelastic Strong Internal Resonance Of Axially Moving Strip Plates

In the field of engineering,many engineering systems,such as maglev train,moving plate belt and current carrying moving wire,belong to the axial moving structure.The mechanical phenomena of axially moving structures under the electromagnetic coupling multi physical field environment have attracted extensive attention of scholars at home and abroad.Therefore,it is of theoretical and practical significance to study the magnetoelastic vibration of axially moving structures.In this paper,the problem of magnetoelastic strong internal resonance of axially moving conducting strip plates is studied.According to the basic theories of elastic mechanics and electromagnetic mechanics,considering the geometric nonlinear factors,based on the relations of kinetic energy,strain energy and external force work of the axial moving plate in the magnetic field,the nonlinear vibration equation of a conducting thin plate moving axially in a magnetic field is derived by using Hamilton variational theory.The main internal resonance of clamped hinged plate in transverse magnetic field is studied.The mechanical model of conducting strip plate in magnetic field is established.The dimensionless nonlinear vibration differential equations are derived by Galerkin integral method,and the amplitude frequency response equations of axially moving conducting strip plate in the state of main internal combined resonance are obtained by multi-scale method.The effects of magnetic field strength,axial velocity,amplitude of external excitation force and axial force on the resonance characteristics and stability of the system are discussed.The magnetoelastic main internal resonance of axially moving plates with elastic supports and linear loads is studied.For the conducting strip plate with elastic support and linear load,by setting the displacement mode function and using Galerkin integral method,the nonlinear vibration differential equations with two degrees of freedom are obtained,and the analytical solution of resonance response is obtained.Through an example,the curve of the first two resonance amplitudes is given,and the effects of different loads andload positions on the vibration characteristics of the system are analyzed.The magnetoelastic combination internal resonance of axially moving plates under double frequency excitation is studied.Considering the second-order displacement mode form,the multi-scale method is used to solve the problem,and the response equations of amplitude frequency of the axially moving conducting strip plate under double frequency excitation are obtained.Through an example,the characteristic curve of amplitude frequency tuning value is given,and the influence of magnetic field strength,axial velocity,amplitude of external excitation force and axial force on resonance amplitude of the system is analyzed.