Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion

Rajneesh Kumar; Tarun Kansal

Volume 29 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(11): 1314-1324

Rajneesh Kumar, Tarun Kansal. Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1314-1324.

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Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion

Department of Mathematics, Kurukshetra University, Kurukshetra-136 119, India

Received Date: 2008-02-07
Rev Recd Date: 2008-09-26
Publish Date: 2008-11-15

Abstract

Abstract

The propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space subjected to stress free, thermally insulated/isothermal and chemical potential boundary conditions, in the context of generalized theory of thermoelastic diffusion is studied. Green and Lindsay(GL) theory, in which, thermodiffusion and thermodiffusion-mechanical relaxations are governed by four different time constants, was selected for study. Secular equations for surface wave propagation in the considered media were derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient were presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equations were also deduced from the present investigation.
- wave propagation,
- transversely isotropic,
- generalized thermoelastic diffusion,
- phase velocity,
- attenuation coefficient

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References(27)

References

[1]	Lord H W, Shulman Y. A generalized dynamical theory of thermoelasticity[J].J Mech Phys Solid,1967,15(5): 299-309. doi: 10.1016/0022-5096(67)90024-5
[2]	Green A E, Lindsay K A. Thermoelasticity[J].J Elasticity,1972,2(1):1-7. doi: 10.1007/BF00045689
[3]	Dhaliwal R S, Sherief H. Generalized thermoelasticity for anisotropic media[J]. Quarterly Appl Math,1980,33:1-8. doi: 10.1093/qjmam/33.1.1
[4]	Chanderashekhariah D S. Thermoelasticity with second: a review[J]. Appl Mech Rev,1986，39(3)：355-376. doi: 10.1115/1.3143705
[5]	Hetnarski R B, Ignaczak J. Generalized thermoelasticity[J].J Thermal Stresses,1999,22(4/5): 451-476. doi: 10.1080/014957399280832
[6]	Nowacki W. Dynamical problems of thermodiffusion in solids—I[J]. Bull Acad Pol Sci Ser Sci Tech,1974,22:55-64.
[7]	Nowacki W. Dynamical problems of thermodiffusion in solids—II[J]. Bull Acad Pol Sci Ser Sci Tech, 1974,22:129-135.
[8]	Nowacki W. Dynamical problems of thermodiffusion in solids—III[J]. Bull Acad Pol Sci Ser Sci Tech,1974,22:275-276.
[9]	Nowacki W. Dynamical problems of thermodiffusion in solids[J].Proc Vib Prob,1974,15:105-128.
[10]	Dudziak W, Kowalski S J. Theory of thermodiffusion for solids[J].Internat J Heat and Mass Transfer,1989,32(11):2005-2013. doi: 10.1016/0017-9310(89)90107-5
[11]	Olesiak Z S, Pyryev Y A. A coupled quasi-stationary problem of thermodiffu-sion for an elastic cylinder[J].Internat J Engrg Sci,1995,33(6): 773-780. doi: 10.1016/0020-7225(94)00099-6
[12]	Sherief H H, Saleh H, Hamza F. The theory of generalized thermoelastic diffusion[J].Internat J Engrg Sci, 2004,42(5/6): 591-608. doi: 10.1016/j.ijengsci.2003.05.001
[13]	Sherief H H, Saleh H. A half space problem in the theory of generalized ther moelastic diffusion[J]. Internat J Solids Structure,2005,42(15): 4484-4493. doi: 10.1016/j.ijsolstr.2005.01.001
[14]	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(2): 159-168. doi: 10.1007/BF02702017
[15]	Singh B. Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion[J].J Sound Vibration, 2006,291(3/5): 764-778. doi: 10.1016/j.jsv.2005.06.035
[16]	Aouadi M. Variable electrical and thermal conductivity in the theory of generalized thermodiffusion[J].ZAMP,2006,57(2):350-366. doi: 10.1007/s00033-005-0034-5
[17]	Aouadi M. A generalized thermoelastic diffusion problem for an infinitely long solid cylinder[J].Internat J Math Math Sci,2006,(13):1-15.
[18]	Aouadi M. A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion[J]. Internat J Solids Structure,2007,44(17): 5711-5722. doi: 10.1016/j.ijsolstr.2007.01.019
[19]	Aouadi M. Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion[J].J Thermal Stresses, 2007,30(7):665-678. doi: 10.1080/01495730701212815
[20]	Aouadi M. Generalized theory of thermoelastic diffusion for anisotropic media[J]. J Thermal Stresses, 2008,31(3): 270-285. doi: 10.1080/01495730701876742
[21]	Sharma J N, Walia V, Gupta S K. Effect of rotation and thermal relaxations on Rayleigh waves in piezothermoelastic half space[J].Internat J Mech Sci, 2008,50(3): 433-444. doi: 10.1016/j.ijmecsci.2007.10.001
[22]	Sharma J N. Generalized thermoelastic diffusive waves in heat conducting materials[J].J Sound Vibration,2007,301: 979-993. doi: 10.1016/j.jsv.2006.11.001
[23]	Sharma J N, Sharma Y D, Sharma P K. On the propagation of elasto- thermodiffusive surface waves in heat-conducting materials[J].J Sound Vibration, 2008,351(4): 927-938.
[24]	Kumar R, Kansal T. Propagation of Lamb waves in transversely isotropic thermo elastic diffusion plate[J].Internat J Solids Structure,2008,4(22/23):5890-5913.
[25]	Sharma J N, Singh D, Kumar R. Generalized thermoelastic waves in transversely isotropic plates[J].Indian J Pure Appl Math,2003,34(6): 841-852.
[26]	Sharma J N, Pal M, Chand D. Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials[J].J Sound Vibration,2005,284(1/2): 227-248. doi: 10.1016/j.jsv.2004.06.036
[27]	Ewing W M, Jardetzky W S, Press F.Elastic Layers in Layered Media[M]. New York, Toronto, London: McGraw-Hill Company, Inc, 1957.

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