Nonlinear Resonance Of A Ferromagnetic Circular Plate Under Electromagnetic Excitation

The circular plate and its combination structures in electromagnetic field environment are widely used in engineering practice,such as iron core of motor stator and rotor,structure parts of electromagnetic sensor,etc.Coupled vibration of these structures in electromagnetic field is an important factor determining the safe operation of electromechanical systems.Therefore,it is of theoretical significance to study the nonlinear vibration of ferromagnetic circular plates in magnetic field,and it can also provide information for the dynamic control of mechanical and electrical systems in engineering practice.In this paper,the nonlinear resonance of ferromagnetic circular plate in electromagnetic field is studied.Based on the theory of thin plate elasticity,the kinetic energy and strain potential energy of ferromagnetic circular plate are given.According to the basic theory of electromagnetism,the magnetic force and Lorentz force on ferromagnetic circular plate in magnetic field are obtained.By means of Hamilton principle,the magnetoelastic coupled nonlinear vibration equation of ferromagnetic circular plate in magnetic field is established.The nonlinear principal resonance of a ferromagnetic circular plate in an alternating magnetic field is studied.Based on the obtained differential equation of circular plate vibration,the Galerkin method is used to discretize the equation,and the corresponding nonlinear forced vibration differential equation under peripheral clamping boundary conditions is derived.The main resonance amplitude-frequency response equation is obtained by using the multi-scale method,and the stability of the solution is analyzed based on Lyapunov theory.The effects of tuning parameters,magnetic field intensity and excitation force on the amplitude are analyzed by examples.The combined resonance of ferromagnetic circular plates under the combined action of electromagnetic force and excitation force is studied.The multi-scale method is used to solve the amplitude-frequency response equation of the system in various combined resonance forms,and the stability of the steady-state solution is analyzed.Through an example,the amplitude-frequency characteristic curve,the curve of amplitude varying with magnetic field intensity and excitation force,and the time-history response diagram,phase diagram and Poincare diagram of system vibration are obtained,and the influence of different parameters on amplitude are analyzed.The main resonance problem and static load effect of a ferromagnetic circular plate in a constant magnetic field are studied.Based on Galerkin method,the initial deflection of ferromagnetic circular plate under static load of constant magnetic field is obtained,and the perturbation differential equation is deduced.The first-order and second-order approximation amplitude-frequency response equations are obtained by the multi-scale method,respectively.The effects of plate thickness,magnetic field strength and excitation force on the resonance amplitude of the system are analyzed by an example.The results of the first-order approximation and the second-order approximation are compared.