关键词: Galerkin原理, Mathieu方程, 薄板, 磁弹性, 稳定性

Abstract: For a current carrying rectangular plate which is simply supported at two opposite boundaries and the other two are fixed, the magnetic-elasticity steady problem is studied. Based on deriving the magnetic-elasticity dynamic buckling equation of the plate applied mechanical load in a magnet field, the buckling equation is changed into the standard form of the Mathieu equation by using Galerkin method. Thus, the buckling problem comes down to solve the Mathieu equation. The criterion equation of the plate at the critical state of magnetic elasticity buckling is obtained with the analysis on the eigen value relations between the coefficients  and  in the Mathieu equation. The map and the boundary lines of the steady areas of the Mathieu equation are shown when  is small exciter. At last, the curves of the relations among the critical state of magnetic elasticity dynamic buckling problem of the plate and the relative parameters are drawn out through a calculating example. The conclusions show that the electrical and magnetic forces may be controlled by changing the parameters of the current and the magnetic field so that the aim for controlling the deformation, stress, strain and the stability of the current carrying plate is achieved.

Key words: Galerkin method, Magnetic-elasticity, Mathieu equation, Stability, Thin plate