轴向运动载流导电板磁热弹性耦合动力学方程

胡宇达; 张金志

doi:10.6052/0459-1879-12-330

轴向运动载流导电板磁热弹性耦合动力学方程

doi: 10.6052/0459-1879-12-330

胡宇达^,,
张金志

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

基金项目: 河北省自然科学基金资助项目(E2010001254).

详细信息

通讯作者:
胡宇达,教授,主要研究方向:磁弹性力学、非线性振动.E-mail:huyuda03@163.com

中图分类号: O332;O442
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- 被引次数: 0
出版历程
- 收稿日期: 2013-04-30
- 修回日期: 2013-05-06
- 刊出日期: 2013-09-18

MAGNETO-THERMO-ELASTIC COUPLED DYNAMICS EQUATIONS OF AXIALLY MOVING CARRY CURRENT PLATE IN MAGNETIC FIELD

Hu Yuda^,,
Zhang Jinzhi

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

Funds: The project was supported by the National Natural Science Foundation of Hebei Province (E2010001254).

摘要

摘要: 针对磁场环境中轴向运动载电流导电板磁热弹性耦合动力学建模问题进行研究. 考虑几何非线性和热效应条件下, 给出薄板运动的动能、应变能以及外力虚功的表达式.应用哈密顿变分原理, 推得力、运动、电、磁和热效应相互作用下轴向运动导电板的非线性磁热弹性耦合振动方程.基于麦克斯韦电磁场方程, 考虑相应的电磁本构关系和电磁边界条件, 推得磁场环境中轴向运动载电流导电板满足的电动力学方程和所受电磁力表达式, 并给出焦耳热作用下耦合形式的热传导方程. 算例表明, 磁场等参量对动力学系统分岔特性有明显影响.所得结果可为此类问题的进一步求解和分析提供理论参考.
- 磁热弹性 /
- 薄板 /
- 轴向运动 /
- 电磁场 /
- 哈密顿原理
Abstract: The theory of In this study, magneto-thermo-elastic coupled dynamics modeling for axially moving carry current plate in magnetic field is investigated. Considering geometric nonlinearity and thermal effect, the expressions of kinetic energy, strain energy and virtual work done by external force were derived. The nonlinear force-electro-magneto- thermo-elastic coupled vibration equations of an axially moving current-conducting thin plate were deduced for the first time in this paper by using Hamilton principle. Based on the Maxwell equations, considering the corresponding electromagnetic constitutive relations and electromagnetic boundary conditions, the electrodynamics equations and electromagnetic forces expressions of axially moving carry current thin plate in general magnetic field were derived and thermal conduction equation caused by Joule heat was also presented. Numerical example shows that magnetic field carries significant effect on the bifurcation characteristics. These results are expected to be a theoretical reference for further analysis of this case.
- magneto-thermo-elastic /
- thin plate /
- axially moving /
- electromagnetic field /
- Hamilton principle

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参考文献(18)

Pao YH, Yeh CS. A linnear theory for soft ferromagnetic elastic bodies. International Journal of Engineering Science, 1973, 11(4): 415-436

Moon FC. Magneto-Solid Mechanics. New York: John Wiley and Sons, 1984

Ambarcumian SA, Bagdasarian GE, Belubekian MV. Magnetoelasticy of Thin Shells and Plates. Moscow: Science, 1977 (in Russian))

Zheng XJ, Zhang JP, Zhou YH. Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field. International Journal of Solids and Structures, 2005, 42(8): 2417-2430

Wang XZ, Lee JS, Zheng XJ. Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields. International Journal of Solids and Structures, 2003, 40(22): 6125-6142

Hasanyan DJ, Librescu L, Ambur DR. Bucking and postbuckling of magnetoelastic flat plates carrying an electric current. International Journal of Solids and Structures, 2006, 43(16): 4971-4996

Gao YW, Xu B, Huh H. Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields. Acta Mechanica, 2010, 210(1-2): 99-116

Hu YD, Li J. Nonlinear magnetoelastic vibrating equations and resonance analysis of current-conducting thin plate. International Journal of Structural Stability and Dynamics, 2008, 8(4): 597-613

Hu YD, Li J. The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic filed. Journal of Sound and Vibration, 2009, 319(3-5): 1107-1120

Hu YD, Li J. Magneto-elastic combination resonances analysis of current-conducting thin plate. Applied Mathematics and Mechanics, 2008, 29(8): 1053-1066

Pellicano F. On the dynamic properties of axially moving systems. Journal of Sound and Vibration, 2005, 281(3-5): 593-609

陈树辉, 黄建亮. 轴向运动梁非线性振动内共振研究. 力学学报, 2005, 37(1): 57-63 (Chen Shuhui, Huang Jianliang. On internal resonance of nonlinear vibration of axially moving beams. Acta Mechanica Sinica, 2005, 37(1): 57-63 (in Chinese))

陈立群, 吴俊. 轴向变速运动黏弹性弦线的横向振动分岔. 固体力学学报, 2005, 26(1): 83-86 (Chen Liqun, Wu Jun. Bifurcation in transverse vibration of axially accelerating viscoelastic strings. Acta Mechanica Solida Sinica, 2005, 26(1): 83-86 (in Chinese))

Yang XD, Chen LQ. Dynamic stability of axially moving viscoelastic beams with pulsating speed. Applied Mathematics and Mechanics, 2005, 26(8): 989-995

刘彦琦, 张伟, 高美娟等. 基于积分本构黏弹性带的横向非线性动力学. 力学学报, 2008, 40(3): 421-432 (Liu Yanqi, Zhang Wei, Gao Meijuan, et al. Transverse nonlinear nonplanar dynamics of an axially moving viscoelastic belt with integral constitutive law. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(3): 421-432 (in Chinese))

Banichuk N, Jeronen J, Neittaanmäki P, et al. On the instability of an axially moving elastic plate. International Journal of Solids and Structures, 2010, 47(1): 91-99

Joohong K, Jooyong C, Usik L, et al. Modal spectral element formulation for axially moving plates subjected to in-plane axial tension. Computers and Structures, 2003, 81(20): 2011-2020

钱伟长. 变分法及有限元(上册). 北京: 科学出版社, 1980 (Qian Weichang. Variational Method and Finite Element Method (Volume 1). Beijing: Science Press, 1980 (in Chinese))

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