四边简支载流纳米板的磁弹性稳定问题分析
Analysis of magneto-elastic stability of current-carrying nanoplates with four edges simply supported
查看参考文献18篇
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文摘
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研究四边简支载流纳米板在电磁场及机械载荷作用下的磁弹性稳定问题。结合非局部理论与板壳磁弹性理论,导出考虑尺度效应的纳米板的磁弹性动力学方程,得出载流纳米板在磁场及机械载荷作用下的磁弹性动力稳定方程;利用伽辽金原理将稳定性方程整理为特殊函数马丢方程的标准形式,根据其系数的本征值关系,判别磁弹性稳定问题的最低失稳临界状态;通过数值模拟得到纳米板失稳临界电流密度与相关参数之间的关系图及变化规律。结果表明:磁感应强度、板长与板厚、外加机械载荷及小尺度参数均会影响纳米板的稳定性;当小尺度参数取1nm时,板长在200nm~450nm、板厚在1nm~10nm的区间内,纳米板的稳定性随着磁感应强度、板长及板厚的变化而急剧变化。在这个灵敏区间内改变磁感应强度、板长及板厚的大小,可以有效地提高纳米板的稳定性。 |
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其他语种文摘
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Under electromagnetic and mechanical loads, the magneto-elastic stability of a current-carrying nano-plate with four sides simply supported is studied. Firstly, combining the nonlocal theory and the magneto-elastic theory of plates and shells, the magneto-elastic dynamic equations of nanoscale plate which considered the scale effects are derived, and the magneto-elastic dynamic stability equation of the current-carrying nano-plate under electromagnetic and mechanical loads are obtained. Then applying Galerkin's principle, the stability equation is expressed as the standard form of special function Mathieu equation. According to the eigenvalues relation of the coefficients in Mathieu equation, the minimum critical instable state of magneto-elastic stability problem is determined. Finally, the relationship between critical current density and related parameters of nano-plate is obtained through numerical simulation. The results show that the stability of nanoplates is affected by magnetic induction intensity, plate length and thickness, applied mechanical loads and small scale parameters. When the small scale parameter is lnm, the stability of the nanoplate varies sharply with the change of magnetic induction intensity, plate length in the range of 200nm~450nm and plate thickness in the range of 1nm~10nm. Changing the magnetic induction intensity, plate length and plate thickness in this sensitive range can effectively improve the stability of nanoplates. |
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来源
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应用力学学报
,2020,37(5):1900-1906 【核心库】
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DOI
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10.11776/cjam.37.05.d058
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关键词
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纳米板
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尺度效应
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磁弹性
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稳定性
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马丢方程
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地址
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1.
燕山大学建筑工程与力学学院, 秦皇岛, 066004
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燕山大学, 河北省重型装备与大型结构力学可靠性重点实验室, 秦皇岛, 066004
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中国科学院力学研究所, 非线性力学国家重点实验室(LNM), 北京, 100080
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1000-4939 |
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学科
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力学;物理学 |
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基金
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河北省自然科学基金
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河北省高等学校科学研究青年基金
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北京大学湍流与复杂系统国家重点实验室开放课题
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文献收藏号
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CSCD:6829704
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参考文献 共
18
共1页
|
|
1.
韩光平.
微电子机械系统力学性能及尺寸效应研究,2006
|
被引
4
次
|
|
|
|
|
2.
康新. 基于Cosserat理论的微梁振动特性的尺度效应.
机械强度,2007,29(1):1-4
|
被引
13
次
|
|
|
|
|
3.
王炳雷.
微结构尺寸效应研究及其应用,2011
|
被引
2
次
|
|
|
|
|
4.
Li C. Vibrational responses of micro/nanoscale beams:size-dependent nonlocal model analysis and comparisons.
Journal of mechanics,2015,31(1):7-19
|
被引
1
次
|
|
|
|
|
5.
李明. 磁敏固支载流单壁碳纳米管在轴向磁场中的振动特性.
应用力学学报,2017,34(4):634-640
|
被引
6
次
|
|
|
|
|
6.
Shahrokh H H. Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory.
Physica E:low-dimensional systems and nanostructures,2011,43(7):1400-1404
|
被引
3
次
|
|
|
|
|
7.
刘辰.
非局部压电纳米板的振动和稳定性研究,2016
|
被引
4
次
|
|
|
|
|
8.
Wolfe P. Bifurcation theory of an elastic conducting wire subjected to magnetic forces.
Journal of elasticity,1990,23(2/3):201-217
|
被引
1
次
|
|
|
|
|
9.
Gao Yuanwen. Numerical analysis on magnetic-elastoplastic buckling and bending of ferromagnetic rectangular plate.
International journal of modern physics B,2008,22(31/32):6212-6217
|
被引
1
次
|
|
|
|
|
10.
Van Lieshout P H. A variational principle for magneto-elastic buckling.
Journal of engineering mathematics,1987,21(3):227-252
|
被引
3
次
|
|
|
|
|
11.
Shahin F. Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects.
Physica E:low-dimensional systems and nanostructures,2018,97:191-205
|
被引
1
次
|
|
|
|
|
12.
Van De Ven A A F. Magnetoelastic buckling of thin plates in a uniform transverse magnetic field.
Journal of elasticity,1978,8(3):297-312
|
被引
2
次
|
|
|
|
|
13.
Yang Wentao. Buckling of a ferromagnetic thin plate in a transverse static magnetic field.
Chinese science bulletin,1998,43(19):1666-1670
|
被引
1
次
|
|
|
|
|
14.
白象忠.
板壳磁弹性力学基础,2006
|
被引
15
次
|
|
|
|
|
15.
Eringen A C. On nonlocal elasticity.
International journal of engineering science,1972,10(3):233-248
|
被引
58
次
|
|
|
|
|
16.
Eringen A C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves.
Journal of applied physics,1983,54(9):4703-4710
|
被引
155
次
|
|
|
|
|
17.
陈玲. 基于非局部弹性理论的纳米板横向振动.
力学季刊,2016,37(3):485-492
|
被引
5
次
|
|
|
|
|
18.
王知人. 载流薄板磁弹性动力失稳临界状态的判别.
工程数学学报,2006,23(1):133-138
|
被引
1
次
|
|
|
|
|
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