| MAGNETIC-ELASTIC BUCKLING OF A THIN CURRENT CARRYING PLATE SIMPLY SUPPORTED AT THREE EDGES |
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| 作者单位： | WANG Zhiren College of Sciences，Yanshan University，Qinhuangdao 066004，China State Key Laboratory of Nonlinear Continuum Mechanics，Beijing 100080，China WANG Ping BAI Xiangzhong College of Civil Engineering and Mechanics，Yanshan University，Qinhuangdao 066004，China State Key Laboratory of Nonlinear Continuum Mechanics，Beijing 100080，China |
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| 基金项目： | 国家自然科学基金，国家自然科学基金 |
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| 摘 要： | The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin＇s method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients 2 and r/ in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.
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| 关 键 词： | 磁性弹性 方程式 装载板 机械性能 |
MAGNETIC-ELASTIC BUCKLING OF A THIN CURRENT CARRYING PLATE SIMPLY SUPPORTED AT THREE EDGES |
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| Authors: | WANG Zhiren WANG Ping BAI Xiangzhong |
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| Affiliation: | [1]College of Sciences, Yanshan University,Qinhuangdao 066004, China [2]State Key Laboratory of Nonlinear Continuum Mechanics, Beijing 100080, China [3]College of Civil Engineering and Mechanics, Yanshan University,Qinhuangdao 066004, China |
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| Abstract: | The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin's method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients λ and η in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved. |
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| Keywords: | Magnetic-elasticity Lorenz force Buckling Mathieu equation Thin plate |
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