Problem of Rayleigh Wave Propagation in Thermoelastic Diffusion

Document Type: Research Paper


1 Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana , India

2 Indira Gandhi National College, Ladwa(Dhanora), Haryana , India


In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree. The roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically and depicted graphically. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Some particular cases are also deduced from the present investigation.


[1] Eidelman A., Elperin T., Kleeorin N., Krein A., Rogachevskii I., Buchholz J., Gr¨unefeld G., 2004, Turbulent thermal diffusion of aerosols in geophysics and in laboratory experiments, Nonlinear Processes in Geophysics 11: 343-350.
[2] Eftimie S., Rusu A., Ionescu A.M., 2010, The drift/diffusion ratio of the mos transistor drain current, UPB Scientific Bulletin, Series C 72(2): 77-88.
[3] Gekas V., Öste R., Lamberg I., 1993, Diffusion in heated potato tissue, Journal of Food Science 58(4): 827-831.
[4] Podstrigach Y. S., 1961, Differential equations of the problem of thermodiffusion in isotropic deformable solid, Dopovidi Academii Nauk Ukrain SSR 2:169-172.
[5] Podstrigach Y. S., Pavlina V. S., 1965, Differential equations of thermodynamic processes in n-component solid solutions, Fiziko-khimicheskaya Mekhanika Materialov 1(4): 259-264.
[6] Podstrigach Y. S., 1964, The diffusion theory of strain of an isotropic solid medium, Vopr. Mekh. Real. Tver. Tela 2: 71-99.
[7] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid – I, Bulletin of Polish Academy of Sciences Technical Sciences 22: 55-64.
[8] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid-II, Bulletin of Polish Academy of Sciences Technical Sciences 22: 129-135.
[9] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid-III, Bulletin of Polish Academy of Sciences Technical Sciences 22: 275-276.
[10] Nowacki W., 1974, Dynamic problems of thermodiffusion in solids, Processing Vibration Problems 15: 105-128.
[11] Sherief H.H., Saleh H., 2005, A half space problem in the theory of generalized Thermoelastic diffusion, International Journal of Solids and Structures 42: 4484-4493.
[12] Kumar R., Kansal T., 2008, Propagation of lamb waves in transversely isotropic thermoelastic diffusive plate, International Journal of Solids and Structures 45: 5890-5913.
[13] Sharma J.N., 2007, Generalized thermoelastic diffusive waves in heat conducting materials, Journal of Sound and Vibration 301: 979-993.
[14] Sharma J.N., Sharma Y.D., Sharma P.K., 2008, On the propagation elasto-thermodiffusive surface waves in heat-conducting materials, Journal of Sound and Vibration 315(4): 927-938.
[15] Kumar R., Gupta V., 2013, Uniqueness and reciprocity theorem and plane waves in thermoelastic diffusion with a fractional order derivative, Chinese Physics B 22(7):74601.
[16] Allam A., Omar M., Ramadan K., 2014, A thermoelastic diffusion interaction in an infinitely long annular cylinder, Archive of Applied Mechanics 84(7): 953-965.
[17] Kumar R., Kansal T., 2008, Effect of rotation on Rayleigh waves in an isotropic generalized thermoelastic diffusive half-space, Archives of Mechanics 60: 421-443.
[18] Kumar R., Kansal T., 2009, Propagation of Rayleigh waves in transversely isotropic generalized thermoelastic diffusion, Journal of Engineering Physics and Thermophysics 82: 1199-1210.
[19] Abouelregal A.E., 2011, Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model, International Journal of Engineering Science 49: 781-791.
[20] Sharma M.D., 2014, Propagation and attenuation of Rayleigh waves in generalized thermoelastic media, Journal of Seismology 18: 61-79.
[21] Ewing W.M., Jardetzky W.S., Press F., 1957, Elastic Layers in Layered Media, McGraw-Hill Company, Inc., New York, Toronto, London.