In this paper, based on the nonlinear magneto-elastic kinetic equation and the electrodynamics equation of the thin current-carrying plate, the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method. Using the differ- ence method and quasi-linearization method, the nonlinear magneto-elastic equa- tions were reduced to a sequence of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization.

At first,based on nonlinear magnetic-elasticity kinetic equations,physical equations,geometric equations,the expressions of Lorentz forces and electrodynamics equations,the magnetic-elasticity kinetic steady equation of the problem were derived. Then,the equation was changed into the standard form of the Mathieu equation using Galerkin method. So,the stability problem is transformed to solve a Mathieu equation.

In this paper, the nonlinear magneto-elastic kinetic equations, the geometric equations, the physical equations and the electrodynamics equations of thin current-carrying strip-plate under the action of the coupled field are given, and the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method.

Based on the nonlinear magneto-elastic kinetic equations and the electrodynamics equations of thin current-carrying plates, the nonlinear differential equations of normal Cauchy type, which includes ten basic unknown functions, are obtained by means of variable replacement method.

The nonlinear magnetoelastic kinetic equations,the electrodynamics equations and the expressions of Lorentz force of thin current-carrying plate under the action of the coupled field are given. The normal Cauchy form nonlinear differential equations,which include ten basic unknown functions in all,are obtained by means of variable replacement.

The magnetic-elasticity stability problem of a current plate clamped at each edge,which is under the action of mechanical load in magnetic field,was studied by using the stability of Mathieu equation's solution in this paper.At first,based on nonlinear magnetic-elasticity kinetic equations,physical equations,geometric equations,the expressions of Lorentz forces and electrodynamics equations,the magnetic-elasticity kinetic steady equation of the problem were derived.Then,the equation was changed into the standard...

The magnetic-elasticity stability problem of a current plate clamped at each edge,which is under the action of mechanical load in magnetic field,was studied by using the stability of Mathieu equation's solution in this paper.At first,based on nonlinear magnetic-elasticity kinetic equations,physical equations,geometric equations,the expressions of Lorentz forces and electrodynamics equations,the magnetic-elasticity kinetic steady equation of the problem were derived.Then,the equation was changed into the standard form of the Mathieu equation using Galerkin method.So,the stability problem is transformed to solve a Mathieu equation.By discussing the eigenvalue relation of the coefficient λ and η in Mathieu equation,means determining the boundary lines between the steady and unsteady solution areas of Mathieu equation, the criterion equation of the problem is presented here.As an example,a current plate clamped at each edge was solved.The curves of the relations among the parameters when the plate is in the critical situation of steady are shown in the paper.The calculated answers and the regularity of parameters variation are also discussed.

In this paper, the nonlinear magneto-elastic kinetic equations, the geometric equations, the physical equations and the electrodynamics equations of thin current-carrying strip-plate under the action of the coupled field are given, and the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method. Using the difference method and quasi-linearization method, the nonlinear magneto-elastic equations were reduced to...

In this paper, the nonlinear magneto-elastic kinetic equations, the geometric equations, the physical equations and the electrodynamics equations of thin current-carrying strip-plate under the action of the coupled field are given, and the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method. Using the difference method and quasi-linearization method, the nonlinear magneto-elastic equations were reduced to a sequence of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization. Through specific example, the numerical solutions of the stresses and deformations in the thin current-carrying strip-plate mixed with fixed and simply supported edges were obtained. The results that the stresses and deformations of the thin current-carrying strip-plate mixed with fixed and simply supported edges are altered with the variation of the electromagnetic parameters were discussed. Through a special case, it is shown that the deformations of the strip-plate can be controlled by changing the electromagnetic parameters.

Based on the nonlinear magneto-elastic kinetic equations and the electrodynamics equations of thin current-carrying plates, the nonlinear differential equations of normal Cauchy type, which includes ten basic unknown functions, are obtained by means of variable replacement method. Using the finite difference method and the quasi-linearization method, the nonlinear magneto-elastic equations are reduced to a series of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization....

Based on the nonlinear magneto-elastic kinetic equations and the electrodynamics equations of thin current-carrying plates, the nonlinear differential equations of normal Cauchy type, which includes ten basic unknown functions, are obtained by means of variable replacement method. Using the finite difference method and the quasi-linearization method, the nonlinear magneto-elastic equations are reduced to a series of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization. Through a specific example, the numerical solutions of the stresses and deformations in thin current-carrying strip-plate with two edges fixed were obtained. The stresses and deformations of thin current-carrying strip-plate with the variation of the electromagnetic parameters are discussed. Through a special case, it is shown that the deformations of the plate can be controlled by changing the electromagnetic parameters.