Magnetoelastic Nonlinear Resonance Of A Rotating Circular Plate

In mechanical engineering, aerospace and other fields, the rotating circular plate is widely used. The mechanical components are often in the electromagnetic field, temperature field and other more complex coupling fields in modern industry. All of these can lead to the rotating circular plate produce complex mechanics behavior which will influence the effect of work. So the research on the rotating circular plate in magnetic field is very important. The nonlinear magnetoelastic resonance and free vibration characteristics of the spinning circular plate were investigated.Based on the theory of large deflection, the expressions of electro-dynamic equations, the expressions of total kinetic energy, potential energy and external force virtual work were derived. The electrodynamics equations, the electromagnetic force and the moment of the circular thin plate were obtained according to the theory of electromagnetic field. The nonlinear magneto-elastic vibration equations of spinning circular thin plate were derived according to Hamilton principle.The resonance of the circular plate subjected to harmonic force was studied. The amplitude-frequency equations of the circular plate were derived based on the Galerkin method and averaging method, the amplitude-frequency equations of the resonance were obtained. The amplitude-frequency characteristic curves and the relation curve of resonance amplitude changing with other physical parameters were obtained. The influence of the thickness, spinning velocity, the magnetic induction intensity and the transverse force on the dynamic characteristics was investigated.The free vibration and the resonance of the circular plate subjected to static load were analyzed. The expression of the frequency and the amplitude-frequency equation of the plate were derived based on the multiple-scale method and the modified multiple-scale method respectively. The relation curves of the frequency changing with the static loads and the other parameters, the amplitude-frequency characteristic curves and the relation curves of the amplitude changing with the magnetic induction and other parameters were obtained. The influence of the spinning velocity, the magnetic induction intensity and static loads and other parameters on the natural frequency and the amplitude of the resonance was investigated.