Rotational Motion Circular Plate Magneto-elastic Nonlinear Harmonic Resonance

In engineering practice,the rotary disk components are widely used,usually engine,turbine,circular saw blade and other important components of the machine,often work in the electromagnetic field,thermal field,mechanical field and other multi-field coupling environment,showing complex dynamic behavior.With the continuous progress of hi-tech field,it is very important to study its complex dynamic behavior.In this paper,the harmonic and combined resonances of rotating circular disk in magnetic field are studied.According to the influence of geometric nonlinearity,the kinetic energy,potential energy,electromagnetic force and external force expression of circular motion thin plate are given based on elastic theory and electromagnetic constitutive relation.Based on the hamilton principle,the nonlinear vibration differential equation of the circular motion disk in the magnetic field is established.The ultraharmonic and subharmonic resonance of circular motion plates in transverse magnetic field is studied.Through the assumption of the mode function and the use of the Galerkin integral method,the dimensionless equation of the rotating plate is obtained.The multi-scale method is used to solve the vibration equation,and the amplitude-frequency response equation of the super-harmonic resonance and sub-harmonic resonance of the rotating disk are obtained.Through the numerical simulation of Matlab,the amplitude-frequency response curves of the amplitude of the rotating plate with the magnetic induction intensity and the amplitude of the excitation force are plotted,and the Poincare diagram,the phase trajectory diagram and the time chart of the motion system are analyzed.Influences of parameters on harmonic resonance of rotating disk are studied.The ultraharmonic-combined resonance problem of rotating circular disk under the combination of two-frequency excitation is studied.The solution of the resonant vibration equation is obtained,and the amplitude-frequency response equation of the resonant disk is obtained.The stability of the solution under steady state motion is analyzed theoretically.Through the numerical calculation,the amplitude-frequency response diagram and the moving-plane map of the rotating circular plate are drawn,and the influence of the vibration parameters on the steady-state solution of the system is analyzed.