MAGNETIC-ELASTISITY STABILITY CRITERION OF THIN CURRENT PLATE SIMPLY SUPORTED AT EACH EDGE
MAGNETIC-ELASTISITY STABILITY CRITERION OF THIN CURRENT PLATE SIMPLY SUPORTED AT EACH EDGE
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DOI：
10.3901/jme.2007.10.155
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发表时间：
2007
影响因子：
4.2
通讯作者：
Wang Zhi-ren;Bai Xiang-zhong;Bian Yu-hong
中科院分区：
文献类型：
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作者：
Wang Zhi-ren;Bai Xiang-zhong;Bian Yu-hong
研究了两相对边界简支且两相对边界固定的载流矩形板的磁弹性稳态问题。在推导磁场作用下受机械载荷作用的板的磁弹性动态屈曲方程的基础上，利用伽辽金法将屈曲方程转化为标准形式的Mathieu方程。因此，屈曲问题归结为求解Mathien方程。通过对Mathieu方程中λ和η的特征值关系的分析，得到了板在电磁弹性屈曲临界状态下的判据方程。在η为小激振器时，给出了Mathieu方程稳定区域的图和边界线。最后，通过算例给出了板的磁弹性动态屈曲问题临界状态与相关参数的关系曲线。结果表明，通过改变电流和磁场的参数，可以控制电磁力，从而达到控制电流夹板的变形、应力、应变和稳定性的目的。
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 Mathien equation.The crite- rion equation of the plate at the critical state of magnetic elas- ticity buckling is obtained with the analysis on the eigen value relations between the coefficientsλandηin the Mathieu equa- tion.The map and the boundary lines of the steady areas of the Mathieu equation are shown whenηis small exciter.At last,the curves of the relations among the critical state of magnetic elastic- ity dynamic buckling problem of the plate and the relative pa- rameters are drawn out through a calculating example.The con- clusions 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 canying plate is achieved.