Study On Magnetoelastic Vibration Of Ferromagnetic Rectangular Plate In Different Magnetic Fields

Ferromagnetic materials in the electromagnetic field will produce complex dynamic behavior,rectangular plate and its composite structure as a widely used in practical engineering components,in the construction,medical equipment,aerospace and other fields occupy an important position.Therefore,it is of great theoretical significance and practical value to study the nonlinear dynamic behavior of rectangular plate under electromagnetic field.In this paper,the magnetoelastic vibration of ferromagnetic rectangular plate in transverse constant magnetic field and alternating magnetic field is studied.Based on the elastic theory of thin plate,the expressions of kinetic energy and potential energy of ferromagnetic rectangular plate are given,and the magnetic force and Lorentz force of ferromagnetic rectangular plate under magnetic field environment are derived from the electromagnetic theory,and the nonlinear magneto-elastic coupling vibration equation of ferromagnetic rectangular plate under magnetic field environment is obtained by using the Hamiltonian variational principle.The nonlinear natural vibration of a rectangular ferromagnetic plate under constant magnetic field is studied.According to the vibration equation of rectangular plate,the Galerkin method was used to separate the time and space variables,and the vibration differential equation under the boundary condition of simply supported with four sides was deduced.Then,the nonlinear natural vibration problem was solved with the multi-scale method,and the expression of its natural frequency was obtained.The influences of plate thickness,magnetic field,initial value and side length ratio on the natural frequency of rectangular plate are analyzed by an example,and the differences of natural vibration characteristics of three kinds of materials are discussed.The nonlinear primary resonance of a rectangular ferromagnetic plate subjected to transverse harmonic excitation in an alternating magnetic field is studied.Based on the obtained vibration equation of rectangular plate,the Galerkin method was used to discretize the variables,and the forced vibration differential equation of rectangular plate was deduced.The amplitude-frequency response equation of the primary resonance of the system is obtained by using the multi-scale method,and the stability of the solution is analyzed according to Lyapunov theory.The effects of tuning parameters,plate thickness,magnetic field,plate width and excitation force on the primary resonance of the system are analyzed by numerical examples.Forced vibration of ferromagnetic rectangular plate in constant magnetic field under different boundary conditions is studied.The vibration differential equation is obtained by Galerkin method.The special solution of the equation is obtained and the expressions of amplification factor,frequency ratio and phase difference between response and excitation are given.The effects of magnetic field intensity,plate thickness and plate width on the amplification factor and the amplitude of rectangular plate are analyzed by an example,and the effects of three boundary conditions on the vibration characteristics of the system are compared.