Nonlinear Parametric Resonance Of Axially Accelerating And Current-carrying Beam

The vibration of axially moving structures has been widely studied by scholars both at home and abroad and lots of achievements are obtained.With the wide application of conductive and magnetic materials in heavy equipment manufacturing,aerospace,transportation and other important areas,the study on the nonlinear vibration of axially moving current carrying structures in magnetic field has its practical value and significance.However,the study on the vibration problem of the axial current in the magnetic field is very rare at present.In this paper,the nonlinear parametric resonance of the axially accelerating and current-carrying beam was studied.Based on the basic theory of elastic mechanics and electromagnetic field,the basic expressions of kinetic energy,potential energy,mechanical force and electromagnetic force were given,and then the nonlinear magnetoelastic coupling vibration equation of the axially accelerating and current-carrying beam was derived by applying the Hamilton variational principle.The problem of the primary resonance-principal parametric resonance of an axially accelerating and current-carrying beam simply supported at two ends was investigated.The magneto-elastic vibration differential equation was obtained by using Galerkin integral method.Then the multiscale method and coordinate transformation method were utilized and the amplitude-frequency response equation was obtained.And the effect of detuning parameter,axial velocity,axial tension,magnetic induction intensity,electric current density,static load,moving load and forced excitation on the resonance characteristics by using Matlab.The principal parametric resonance of the axially accelerating and current-carrying beam subjected to static load and the primary resonance-principal parametric resonance of an axially accelerating and current-carrying beam subjected to static load were investigated.By applying Galerkin integral method and multi-scale method,the nonlinear primary parametric response amplitude-frequency equation using the static load as a parameter was achieved.And the stability of steady-state solution was also discussed.The influence of magnetic induction intensity,static load and other parameters on the dynamic behavior of parametric resonance system was analyzed by numerical calculation.The primary resonance-principal parametric resonance of an axially moving and current-carrying beam subjected to moving load was investigated.The mechanical model of an axially moving and current-carrying beam subjected to moving load in the magnetic field was established.By applying Galerkin integral method and multi-scale method,the nonlinear primary parametric response amplitude-frequency equation using the moving load as a parameter was achieved.The influence of axial tension,moving load and other parameters on the dynamic behavior of the parametric system was analyzed by numerical calculation.