轴向运动导电导磁梁的磁弹性振动方程

胡宇达; 张立保

doi:10.3879/j.issn.1000-0887.2015.01.006

轴向运动导电导磁梁的磁弹性振动方程

doi: 10.3879/j.issn.1000-0887.2015.01.006

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,河北秦皇岛 066004

基金项目: 国家自然科学基金(11472239)；河北省高等学校科学技术研究重点项目(ZD20131055)

详细信息

作者简介:
胡宇达（1968—），男，黑龙江人，教授，博士，博士生导师(通讯作者. E-mail: huyuda03@163.com).

中图分类号: O322;O442
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出版历程
- 收稿日期: 2014-06-10
- 修回日期: 2014-10-06
- 刊出日期: 2015-01-15

Magneto-Elastic Vibration Equations for Axially Moving Conductive and Magnetic Beams

Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province, Yanshan University, Qinhuangdao 066004, P.R.China

Funds: The National Natural Science Foundation of China(11472239)

摘要

摘要: 针对磁场环境中轴向运动导电导磁梁磁弹性耦合振动的理论建模问题进行研究.基于Timoshenko(铁木辛柯)梁理论并考虑几何非线性因素，给出轴向运动弹性梁在横向双向振动下的形变势能、动能计算式以及电磁力和机械力的虚功表达式.应用Hamilton(哈密顿)变分原理，推得磁场中轴向运动Timoshenko梁的非线性磁弹性耦合振动方程，并给出了简化形式的Euler-Bernoulli(欧拉伯努利)梁磁弹性振动方程.根据电磁理论和相应的电磁本构关系，得到载流导电弹性梁所受电磁力的表达式，基于磁偶极子-电流环路模型给出铁磁弹性梁所受磁体力和磁体力偶的表述形式.通过算例，分析了轴向运动导电弹性梁的奇点分布及其稳定性问题.
- 导电导磁梁 /
- 磁弹性 /
- 振动 /
- 轴向运动 /
- Hamilton原理
Abstract: The magneto-elastic coupled vibration theoretical model for axially moving conductive and magnetic beams in magnetic field environment was studied. Based on the Timoshenko beam theory and with the geometric nonlinearity considered, the expressions for the deformation potential energy, kinetic energy, electromagnetic force and the virtual work of mechanical force of the elastic beam in axial motion and lateral bidirectional vibration were gained. Then the Hamilton variational principle was applied to get the nonlinear magneto-elastic coupled vibration equations for the axially moving Timoshenko beam in a magnetic field, and get those for the simplified Euler-Bernoulli beam. Based on the electromagnetic theory and the constitutive relation of the corresponding electromagnetism, the expressions for the electromagnetic force of the current-conducting elastic beam, and for the magnet force and magnet force couple of the magneto-elastic beam based on the magnetic dipole-current loop model, were derived. Through the numerical example, the singularity distribution and stability of the conductive and elastic beam in axial movement were analyzed.
- conductive and magnetic beam /
- magneto-elastic /
- vibration}axially moving /
- Hamilton principle /

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参考文献(14)

[1]	CHEN Li-qun, TANG You-qi, Limc C W. Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams[J].Journal of Sound and Vibration,2010,329(5): 547-565.
[2]	DING Hu, CHEN Li-qun. Galerkin methods for natural frequencies of high-speed axially moving beams[J].Journal of Sound and Vibration,2010,329(17): 3484-3494.
[3]	CHEN Shu-hui, HUANG Jian-liang, Sze K Y. Multidimensional Lindstedt-Poincaré method for nonlinear vibration of axially moving beams[J].Journal of Sound and Vibration,2007,306(1/2): 1-11.
[4]	陈树辉, 黄建亮. 轴向运动梁非线性振动内共振研究[J]. 力学学报, 2005,37(1): 57-63.(CHEN Shu-hui, HUANG Jian-liang. On internal resonance of nonlinear vibration of axially moving beams[J].Acta Mechanica Sinica,2005,37(1): 57-63.(in Chinese))
[5]	Ghayesh M H, Kafiabad H A, Tyler R. Sub and super-critical nonlinear dynamics of a harmonically excited axially moving beam[J].International Journal of Solids and Structures,2012,49(1): 227-243.
[6]	Pakdemirli M, Boyacm H. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity[J].International Journal of Non-Linear Mechanics,2001,36(1): 107-115.
[7]	Ozkaya E, Pakdemirli M. Vibrations of an axially accelerating beam with small flexural stiffness[J].Journal of Sound and Vibration,2000,234(3): 521-535.
[8]	WU Guan-yuan. The analysis of dynamic instability on the large amplitude vibrations of a beam with transverse magnetic fields and thermal loads[J].Journal of Sound and Vibration,2007,302(1/2): 167-177.
[9]	Pratiher B. Non-linear response of a magneto-elastic translating beam with prismatic joint for higher resonance conditions[J].International Journal of Non-Linear Mechanics,2011,46(5): 685-692.
[10]	Pratiher B, Dwivedy S K. Non-linear dynamics of a soft magneto-elastic Cartesian manipulator[J].International Journal of Non-Linear Mechanics,2009,44(7): 757-768.
[11]	HU Yu-da, ZHANG Jin-zhi. Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field[J].Applied Mathematics and Mechanics(English Edition),2013,34(11): 1405-1420.
[12]	胡宇达. 轴向运动导电薄板磁弹性耦合动力学理论模型[J]. 固体力学学报, 2013,34(4): 417-425.(HU Yu-da. Magneto-elastic coupled dynamics theoretical model of axially moving current-conducting thin plate[J].Chinese Journal of Solid Mechanics,2013,34(4): 417-425.(in Chinese))
[13]	Dym C L, Shames I H. 固体力学变分法[M]. 袁祖贻, 姚金山, 应达之译. 北京: 中国铁道出版社, 1984.(Dym C L, Shames I H.Solid Mechanics: A Variational Approach [M]. YUAN Zu-yi, YAO Jin-shan, YING Da-zhi transl. Beijing: Chinese Railway Publishing House.(in Chinese))
[14]	周又和, 郑晓静. 铁磁体磁弹性相互作用的广义变分原理与理论模型[J]. 中国科学, A辑, 1999,29(1): 61-68.(ZHOU You-he, ZHENG Xiao-jing. A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies[J].Science in China, Series A,1999,29(1): 61-68.(in Chinese))