Nonlinear Resonance Of Axially Moving Conductive Elastic Beam In Magentic Field

At present, research on the dynamic characteristics of the axial moving structures has become increasingly mature, the mechanical behavior of electromagnetic solid structures in the multi-field coupling condition has also aroused extensive attentions. Therefore, research work on dynamic behavior of axially moving conductive elastic beam in the magnetic field gradually getting people’s attention. In this paper magneto-elastic resonance problem of axial moving conductive elastic beam is investigated.Based on Euler-Bernoulli beam elastic theory and electromagnetic field theory, considering the geometric nonlinearity, the nonlinear vibration equation of axial moving conductive elastic beam is developed by Hamilton principle in a magnetic field.The magneto-elastic primary resonance of axially moving current-carrying beams in magnetic field was investigated. Considering the hinged-hinged boundary condition, three order displacement mode function is assumed. The magneto-elastic vibration differential equation of beams was obtained through the application of Galerkin integral method. Based on the method of multiple-scale, the principal resonance amplitude-frequency response equation of external excitation and applied current interaction system were gained. Then influence of the magnetic field strength, the applied current, axial velocity, external motivation on the amplitude of system resonance were analyzed. The results show that in the curve of amplitude-intensity of magnetic field, with the increase of tuning parameters resonance, the curve gradually retracted and its upper final closed, the critical separation point "shifted" to the right by the applied current in this process.The magneto-elastic internal resonance and primary-internal resonance of axially moving conductive beams in magnetic field were studied. Considering the fix-hinged boundary condition, two order displacement mode function is assumed. Based on the method of multiple-scale and Galerkin integral method, the coupled amplitude equations of 1:3 internal resonance system and amplitude-frequency response equations of primary-internal resonance system were obtained. By programming calculation, the coupling relationship between the first and the second order vibration modes be obtained in the no damping resonance system and the modal amplitude attenuation be obtained in the damping resonance system. Then the influences of initial conditions, the axial velocity, the external magnetic field strength and the tuning parameter on the vibration modes are revealed in detail. Amplitude-frequency characteristic curves and the relation curve charts of resonance amplitude and other physical parameters were obtained at the same time. Then the effects of axial velocity, tuning parameters, external magnetic field strength, external excitation force and external current on the dynamic characteristics of the system are analyzed. Finally, we discuss the stability of the solution.