Nonlinear Magnetoelastic Resonance Of Axially Moving Conductive Beam Between Parallel Wires

The axially moving structure exists widely in engineering area,the vibration stability of the axially moving system affects the safety and reliability of the whole system,especially in the environment of electromagnetic coupling multi-physical field,the dynamic phenomenon of electromagnetic structure model in the electromagnetic field has aroused great interest from domestic and foreign scholars.Therefore,it is of great theoretical significance to study the magneto-elastic vibration problem of axially moving structures.This paper mainly analyzes the problem of nonlinear magneto-elastic vibration in a magnetic field generated by a parallel conducting wire in an axially moving conductive beam.For axially moving conductive beams in magnetic field environment,according to the basic theory of elastic mechanics and electromagnetic mechanics,considering the geometric nonlinear term,based on the kinetic energy,strain energy,external force virtual work and imaginary work of the axially moving beam,the nonlinear magneto-elastic vibration equation of the axially moving beam in the magnetic field is derived by using the Hamilton principle.Magneto-elastic primary resonance of an axially moving current-carrying beam is investigated,where the beam move between two parallel and infinite long straight current-carrying wires.The non-dimensional nonlinear differential equation of axially moving beam is obtained by means of Galerkin method.The approximate analytical solution of first two orders modal nonlinear equation and the primary resonance amplitude frequency response equation are derived by means of the multiple scales method.Through calculation examples,the resonance amplitude of the axially moving current-carrying beam varying with frequency parameters,current-carrying density,current of wire and the position variation relationship are obtained,the effects of various physical and geometric parameters on the resonance characteristics of the system are analyzed.The parametric resonance and principal resonance of the axially moving beam in amagnetic field with periodic variation of the alternating conductor are investigated.By using the Galerkin integral method,the nonlinear parametric-principal resonance differential equation of dimensionless conductive beam is obtained.The vibration equations of nonlinear parameter is derived by using multi-scale method.Through calculation examples,the corresponding amplitude frequency response curves with different frequency parameters,dynamic phase trajectory graph of resonance,as well as the time history response diagrams and phase plot with changing frequency parameters are received,the effects of various physical and geometric parameters on the resonance characteristics of the system are analyzed.The bi-directional coupled vibration of axially moving conductive beams under different current carrying conditions in two-group conductive wires is studied.Assuming the third-order displacement modal function,The transverse bi-directional coupled differential equations of axially moving current-carrying beams under four current-carrying conditions are obtained.By solving the equation numerically,the time history response diagrams,phase and Poincaré maps of the change frequency parameters,beam heights and axial velocities are plotted,and the influence of different parameters on the dynamic characteristics of the system under multi-mode vibration is analyzed.