Magneto-elastic Nonlinear Vibration Of Axially Moving Rectangular Thin Plate

More and more researchers have paid much attention to the dynamic characteristicsof axially moving beam, string, plate and membrane at home and abroad, and there are alarge number of research results in the mechanical behavior of the electromagnetic solidstructure under the multi-field coupling. However, the study on axially moving structure inmagnetic field is rare. In this paper, the nonlinear magnetoelastic parametric resonanceand subharmonic resonance characteristics of the axially moving conductive rectangularplate were investigated.Firstly, based on the theory of electromagnetic field, the expressions of electro-dynamic equations, electromagnetic force and moment of thin plate were obtained, basedon the theory of large deflection, the expressions of total kinetic energy, potential energyand external force virtual work were obtained. The nonlinear magneto-elastic vibrationequations of axially moving rectangular thin plate were further derived by using Hamiltonprinciple.Secondly, according to the problems of the principal parametric resonance of anaxially accelerating rectangular thin plate subjected to parametric excitation, thesimultaneous primary and principal parametric resonance of an axially acceleratingrectangular thin plate subjected to parametric excitation and forced excitation, thesubharmonic resonance of an axially uniform moving rectangular thin plate under thethermal loading and forced excitation. Consider the four sides simply supported boundaryconditions, based on displacement mode hypothesis, by using the Galerkin method andmultiple-scale method, the amplitude-frequency equations of the above three kinds ofresonance were obtained, and the stability of the steady-state motion was also discussed.Finally, as numerical examples for an axially moving rectangular thin plate,amplitude-frequency characteristic curves and the relation curve charts of resonanceamplitude and other physical parameters were was obtained by using Matlab. Theinfluence of detuning parameter, axial speed, axial tension, magnetic induction intensity,transverse harmonic force, thickness of plate and thermal loads on the dynamic characteristics was investigated.