带扩散的广义热弹性固体中移动荷载引起的二维相互作用

S·德斯瓦尔; S·乔德哈瑞

带扩散的广义热弹性固体中移动荷载引起的二维相互作用

S·德斯瓦尔¹,
S·乔德哈瑞²

1.
古鲁詹伯赫希瓦理工大学数学系,海沙125001,哈里亚纳邦,印度;2.戈维特学院数学系,纳尔瓦海沙125037,哈里亚纳邦,印度

详细信息

中图分类号: O343.6；O347.1
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出版历程
- 收稿日期: 2007-06-04
- 修回日期: 2007-11-09
- 刊出日期: 2008-02-15

Two-Dimensional Interactions Due to Moving Load in Generalized Thermoelastic Solid With Diffusion

Sunita Deswal¹,
Suman Choudhary²

1.
Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India;

摘要

摘要: 当一个移动荷载沿着一个坐标轴作用在介质边界上时，研究了该具有广义热弹性扩散的均匀各向同性介质中的扰动．应用特征值逼近方法，研究了Laplace-Fourier变换域中的二维扰动问题．在Fourier扩展技术的基础上，利用Laplace数值逆变换技术，求解了位移分量、应力、温度场、浓度和化学势的解析表达式．数值计算了铜类材料的这些表达式，并给出有关图形．作为特殊情况，给出了广义热弹性介质和弹性介质中，扩散和热效应的理论结果和数值结果．
- 特征值逼近 /
- 矢量矩阵微分方程 /
- 热弹性扩散 /
- 广义热弹性 /
- 移动荷载 /
- Laplace和Fourier变换
Abstract: Disturbances in a homogeneous,isotropic elastic medium with generalized thermoelastic diffusion,when a moving source is acting along one of the co-ordinate axis on the boundary of the medium,are investigated.Eigen value approach was applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem.The analytical expressions for displacement components,stresses,temperature field,concentration and chemical potential were obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques.These expressions were calculated numerically for a copper like material and depicted graphically.As special cases,the results in generalized thermoelastic and elastic media were obtained to depict the diffusion and thermal effects in the medium theoretically and numerically.
- eigen value approach /
- vector matrix differential equation /
- thermoelastic diffusion /
- generalized thermoelasticity /
- moving load /
- Laplace and Fourier transforms

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参考文献(25)

[1]	Biot M.Thermoelasticity and irreversible thermo-dynamics[J].Journal of Applied Physics,1956,27:240-253. doi: 10.1063/1.1722351
[2]	Lord H, Shulman Y. A Generalized thermodynamical theory of thermoelasticity[J].J Mech Phys Solids,1967,15:299-309. doi: 10.1016/0022-5096(67)90024-5
[3]	Dhaliwal R, Sherief H.Generalized thermoelasticity for an isotropic media[J].Quart Appl Math,1980,33:1-8. doi: 10.1093/qjmam/33.1.1
[4]	Sherief H. Fundamental solution of the generalized thermoelastic problem for small time[J].J Thermal Stresses,1986,9:151-164. doi: 10.1080/01495738608961894
[5]	Sherief H, Anwar M.Problem in generalized thermoelasticity[J].J Thermal Stresses,1986,9:165-181. doi: 10.1080/01495738608961895
[6]	Sherief H, Ezzat M. Solution of the generalized problem of thermoelasticity in the form of series of functions[J].J Thermal Stresses,1994,17:75-95. doi: 10.1080/01495739408946247
[7]	Sherief H, Anwar M.State space approach to two-dimensional generalized thermoelasticity problems[J].J Thermal Stresses,1994,17:567-590. doi: 10.1080/01495739408946280
[8]	Sinha A N, Sinha S B. Reflection of thermoelastic waves at a solid half-space with thermal relaxation[J].J Phys Earth,1974,22:237-244. doi: 10.4294/jpe1952.22.237
[9]	Abd-Alla A N, Al-Dawy A A. The reflection phenomena of SV waves in a generalized thermoelastic medium[J].Internat J Math Sci,2000,23:529-546. doi: 10.1155/S0161171200004221
[10]	Sharma J N, Kumar V, Chand D. Reflection of generalized thermoelastic waves from the boundary of a half-space[J].J Thermal Stresses,2003,26:925-942. doi: 10.1080/01495730306342
[11]	Oriani R A. Thermomigration in solid metals[J].J Phys Chem Solids,1969,30:339-351. doi: 10.1016/0022-3697(69)90315-1
[12]	Fryxel R E, Aitken E A.High temperature studies of urania in a thermal gradient[J].J Nucl Mater,1969，30: 50-56. doi: 10.1016/0022-3115(69)90167-6
[13]	Nowacki W. Dynamic problems of thermoelastic diffusion in solids-Ⅰ[J].Bulletin de l'Academic Polonaise des Sciences Serie des Sciences Techniques,1974,22:55-64.
[14]	Nowacki W. Dynamic problems of thermoelastic diffusion in solids-Ⅱ[J].Bulletin de l'Academic Polonaise des Sciences Serie des Sciences Techniques,1974,22:129-135.
[15]	Nowacki W. Dynamic problems of thermoelastic diffusion in solids-Ⅲ[J].Bulletin de l'Academic Polonaise des Sciences Serie des Sciences Techniques,1974,22:266-275.
[16]	Nowacki W. Dynamic problems of diffusion in solids[J].Eng Frac Mech,1976,8:261-266. doi: 10.1016/0013-7944(76)90091-6
[17]	Sherief H, Hamza F,Saleh H.The theory of generalized thermoelastic diffusion[J].Internat J Eng Sci,2004,42:591-608. doi: 10.1016/j.ijengsci.2003.05.001
[18]	Singh B. Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion[J].J Earth Syst Sci,2005,114: 159-168. doi: 10.1007/BF02702017
[19]	Sherief H，Saleh H. A half-space problem in the theory of generalized thermoelastic diffusion[J].Internat J Solid Structures,2005,42:4484-4493. doi: 10.1016/j.ijsolstr.2005.01.001
[20]	Aouadi M. Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion[J].Zeitschrift fr Angewandte Mathematik und Physik(ZAMP),2006,57(2):350-366. doi: 10.1007/s00033-005-0034-5
[21]	Aouadi M. A generalized thermoelastic diffusion problem for an infinitely long solid cylinder[J].Internat J Mathematics and Mathematical Sci,2006，2006:123-137.
[22]	Verrujit A, Cordova C. Moving loads on an elastic half plane with hysteretic damping[J].J Appl Mech,2001,68:915-922. doi: 10.1115/1.1410097
[23]	Honig G, Hirdes U. A method for the numerical inversion of the Laplace transform[J].J Comp Appl Math,1984,10:113-132. doi: 10.1016/0377-0427(84)90075-X
[24]	Press W H, Teukolsky S A, Vellerlig W T,et al.Numerical Recipes in FORTRAN[M].2nd Ed . Cambridge: Cambridge University Press, 1986.
[25]	Thomas L.Fundamentals of Heat Transfer[M].Englewood Cliffs, New Jersey: Prentice-Hall Inc, 1980.