Stability Analysis Of Current Carrying Thin Plate In Magnetic Field

The sheet has been widely used in practical engineering,and in-depth study about the nonlinear dynamic characteristics of thin plate in the electromagnetic environment,but the study of stochastic bifurcation plate in electromagnetic field and mechanical field coupling under the action of the very rare on the report,so in the dynamics of the environment in different plate study room is necessary.This paper studied the stability problem in electromagnetic field and mechanical field of rectangular thin current carrying plate,using the Galerkin variational method will thin nonlinear motion equations are transformed into stochastic dynamical systems,and using the method of orthogonal polynomial approximation,the random dynamical system into a deterministic system,according to the Jacobian matrix eigenvalue to determine the stability of the system.According to the theory of shell and shell and the basic theory of magnetoelasticity,the nonlinear motion equation of rectangular current-carrying thin plate under the coupling of magnetic field and mechanical field is deduced.Based on the calculation of the rectangular plate with four edges,the four sides of the simply supported,the simply supported and the four sides are fixed at four boundary conditions,the different random vibration equations are established.The Galerkin variational method is used to analyze the vibration equation Into a random differential equation.According to the orthogonal polynomial approximation theory,Hermite orthogonal polynomial is used to transform it into deterministic system.Firstly,the Jacobian matrix of the deterministic system at the equilibrium point is calculated and the eigenvalues of the matrix under different currents are calculated.The stability of the system is judged according to the change of the real part of the eigenvalue.The bifurcation type is determined.Secondly,Finally,the numerical simulation is carried out,and the critical current value of the thin plate is obtained.The influence of the current on the bifurcation is discussed according to the number and the position of the equilibrium point,that is,the influence on the stability of the rectangular thin plate.The results obtained in this paper have some reference value for the reliability design of the thin plate in the coupled field environment.