理想传导弹性体中能量耗散的磁-热-弹性波

P·达斯; M·卡诺利亚

理想传导弹性体中能量耗散的磁-热-弹性波

P·达斯¹,
M·卡诺利亚²

1.
纳塔基沙伯哈斯工学院,加尔各答 700 152,印度;2.加尔各答大学应用数学系,加尔各答 700 009,西孟加拉邦,印度

详细信息

中图分类号: O347.4+2
计量
- 文章访问数: 3015
- HTML全文浏览量: 134
- PDF下载量: 490
- 被引次数: 0
出版历程
- 收稿日期: 2008-02-14
- 修回日期: 2008-12-04
- 刊出日期: 2009-02-15

Magneto-Thermo-Elastic Waves in an Infinite Perfectly Conducting Elastic Solid With Energy Dissipation

Payel Das¹,
M. Kanoria²

1.
Netaji Subhash Engineering College, Technocity, Police Para, Panchpota, Garia, Kolkata-700 152, India;

摘要

摘要: 广义能量耗散弹性理论(TEWED，G-N Ⅲ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究．提出了更普遍的有复杂参数的色散方程，通过运用Leguerre方法解决复杂条件下耦合磁-热-弹性波的问题，表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题．在G-N Ⅲ模型(TEWED)中，耦合磁-热-弹性波传播时发生衰减和色散，扩散的热量由热传播方程中的阻尼项考虑，而在G-N Ⅱ模型没有发生衰减和耗散．最后给出了类铜材料的数值结果．
- 广义热弹性 /
- 磁-热-弹性波 /
- 能量耗散
Abstract: The generalized theory of thermo-elastiaty, r.e., Green and Naghdi (G-N)Ⅲ theory, with energy dissipation(TEWED) is employed in the study of time-harmonic plane wave prpagation in an unbounded, perfectly electxiically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with complex coefficients was obtained for coupled magneto-themlo-elastic wave which is solved in complex domain by using Leguerre's method. It is revealed that the coupled magneto-themlo-elastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity and the external magnetic field. Numerical results for a copper-like material are presented.
- generalized theimoelasticity /
- magneto-thermo-elastic wave /
- energy dissipation

HTML全文

参考文献(23)

[1]	Lord H W, Shulman Y. A generalized dynamical theory of thermoelasticity[J].Journal of Mech Phys Solids,1967,15(5):299-309. doi: 10.1016/0022-5096(67)90024-5
[2]	Green A E, Lindsay K A. Thermoelasticity[J].Journal of Elasticity,1972,2(1):1-7. doi: 10.1007/BF00045689
[3]	Paria G.On magneto-thermo-elastic plane waves[J].Proc Cambridge Philos Soc,1962,58(5):527-531. doi: 10.1017/S030500410003680X
[4]	Nayfeh A, Nemat-Nasser S. Thermo elastic waves in solids with thermal relaxation[J]. Acta Mech,1971,12:43-69.
[5]	Nayfeh A, Nemat-Nasser S. Electro magneto-thermo-elastic plane waves in solid with thermal relaxation[J].J Appl Mech,1972,39(1):108-113. doi: 10.1115/1.3422596
[6]	Roychoudhury S K, Chatterjee(Roy) Gargi. A coupled magnetothermo-elastic problem in a perfectly conducting elastic half-space with thermal relaxation[J].Internat J Math Mech Sci,1990,13(3):567-578.
[7]	Hsieh R K T. Mechanical modelling of new electromagnetic materials[A].In:Proceeding of the IUTAM Symposium on the Mechanical Modelling of New Electromagnetic Materials[C]. Stockholm, Sweden, 2-6 April, 1990.
[8]	Ezzat Magdy A. State space approach to generalized magneto thermo elasticity with two relaxation times in a medium of perfect conductivity[J].Internat J Engrg Sci,1997,35(8):741-752. doi: 10.1016/S0020-7225(96)00112-7
[9]	Ezzat M A, Othman M I, El-Karamany A S.Electromagneto-thermoelastic plane waves with thermal relaxation a medium of perfect conductivity[J].Journal of Thermal Stresses,2001,24(5):411-432. doi: 10.1080/01495730151126078
[10]	Sherief Hany H, Yoset Handy M. Short time solution for a problem in magneto thermoelasticity with thermal relaxation[J].Journal of Thermal Stresses,2004,27(6):537-559. doi: 10.1080/01495730490451468
[11]	Baksi A, Bera R K. Eigen function expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimension[J].Science Direct, Mathematical and Computer Modelling,2005,42:533-552.
[12]	Green A E, Naghdi P M. Thermoelasticity without energy dissipation[J].Journal of Elasticity,1993,31(3):189-208. doi: 10.1007/BF00044969
[13]	Roychoudhuri S K. Magneto-thermo-elastic waves in an infinite perfectly conducting solid without energy dissipation[J].J Tech Phys,2006,47(2):63-72.
[14]	Chandrasekharaiah D S. A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation[J].Journal of Elasticity,1996,43(3):279-283. doi: 10.1007/BF00042504
[15]	Chandrasekharaiah D S. A uniqueness theorem in the theory of thermoelasticity without energy dissipation[J].Journal of Thermal Stress,1996,19(3):267-272. doi: 10.1080/01495739608946173
[16]	Chandrasekharaiah D S, Srinath K S. Thermoelastic interaction without energy dissipation due to a point heat sources[J].Journal of Elasticity,1998,50(2):97-108. doi: 10.1023/A:1007412106659
[17]	Roychoudhuri S K, Dutta P S.Thermo-elastic interaction without energy dissipation in an infinite solid with distributed periodically varying heat source[J].International Journal of Solid Structures,2005,42(14):4192-4203. doi: 10.1016/j.ijsolstr.2004.12.013
[18]	Green A E, Naghdi P M. On undamped heat waves in an elastic solid[J].Journal of Thermal Stress,1992,15(2):251-264.
[19]	Bandyopadhyay N, Roychoudhuri S K. Thermoelastic wave propagation without energy dissipation in an elastic half space[J].Bull Cal Math Soc,2005,97(6):489-502.
[20]	Mallik S H,Kanoria M. A two dimensional problem in generalized thermoelasticity for a rotating orthotropic infinite medium with heat sources[J].Indian J Math,2007,49(1):47-70.
[21]	Banik S, Mallik S H, Kanoria M. Thermoelastic interaction with energy dissipation in an infinite solid with distributed periodically varying heat sources[J].Internat J Pure Appl Math,2007,342:231-246.
[22]	Kar Avijit, Kanoria M. Thermoelastic interaction with energy dissipation in an unbounded body with a spherical hole[J].International Journal of Solids and Structures,2007, 44(9):2961-2971. doi: 10.1016/j.ijsolstr.2006.08.030
[23]	Kar Avijit, Kanoria M. Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc[J]. European Journal of Mechanics Solids, 2007,26(6):969-981. doi: 10.1016/j.euromechsol.2007.03.001