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MAGNETIC-ELASTISITY
STABILITY CRITERION OF THIN
CURRENT PLATE SIMPLY
SUPORTED AT EACH EDGE
WANG Zhiren1, 2 BAI Xiangzhong2, 3
BIAN Yuhong2, 33
(1. College of Sciences, Yanshan University,
Qinhuangdao 066004;
2. State Key Laboratory of Nonlinear Continuum
Mechanics, Beijing 100080;
3. College of Civil Engineering and Mechanics,
Yanshan University, Qinhuangdao 066004)
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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 l and h in the Mathieu
equation. The map and the boundary lines of the steady areas of the
Mathieu equation are shown when h 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 con-trolled 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: Magnetic-elasticity Stability
Mathieu equation Galerkin method Thin plate
CLC No:
O4411
国家自然科学基金(50275128)和河北省自然科学基金(A2006000190)资助项目. Received 20061206, received in revised form 20070418
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