Influences of magnetic field on wave propagation in generalized thermoelastic solid with diffusion

• Autorzy: Abo-Dahab S. M. , Singh B.
• Języki publikacji: PL

Abstrakty

EN

This paper is devoted to estimation of the influence of magnetic field in an elastic solid half-space under thermoelastic diffusion. The governing equations in xz-plane are solved taking into consideration the GL model. The reflection of dilatational (P) wave and shear vertical (SV) wave splits into four waves, namely: P wave, thermal wave, mass diffusion wave and SV wave. The reflection phenomena of P and SV waves from the free surface of an elastic solid with thermoelastic diffusion, under the influence of magnetic field is considered. The expressions for the reflection coefficients for the four reflected waves are obtained. These reflection coefficients are found to depend upon the angle of incidence 0 of P and SV waves, thermoelastic diffusion, magnetic field and other material parameters. The numerical values for the reflection coefficients are calculated analytically and presented graphically for various values of these parameters. Relevant results of previous investigations are deduced as special cases from this study.

Słowa kluczowe

PL

termosprężystość; fala typu P; fala typu SV; pole magnetyczne; dyfuzja masy; współczynnik odbicia

EN

GL model; thermoelasticity; P wave; SV wave; magnetic field; mass diffusion; reflection coefficients

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2009
• Tom: Vol. 61, nr 2
• Strony: 121--136
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Abo-Dahab S. M.

autor

Singh B.

• Mathematics Department, Faculty of Science Qena 83523, South Valley University, Egypt,

Bibliografia

• 1. V. DANILOVSKAYA, Thermal stresses in an elastic half-space due to sudden heating of its boundary, Prikl. Mat. Mekh., 14, 316-324, 1950.
• 2. M.A. BIOT, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 240-253, 1956.
• 3. D.E. CARLSON, Linear thermoelasticity, Handbuch der Physik, Via/2, 97-346, 1972.
• 4. H.W. LORD, Y. SHULMAN, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 7, 71-75, 1967.
• 5. A.E. GREEN, A. LINDSAY, Thermoelasticity, J. Elasticity, 2, 1-7, 1972.
• 6. W. NOWINSKI, Theory of thermoelasticity with applications, Sijthoff and Noordhoof Int., Netherlands, 1978.
• 7. D.S. CHANDRASEKHARAIAH, Thermoelasticity with second sound: A Review, Appl. Mech. Rev., 39, 355-376, 1986.
• 8. R.S. DHALIWAL, H. H. SHERIEF, Generalized thermoelasticity for anisotropic media, Quart. Appl. Math., 33, 1-8, 1980.
• 9. R.B. HETNARSKI, J. IGNACZAK, Generalized thermoelasticity, Journal of Thermal Stresses, 22, 451-476, 1999.
• 10. D. S. CHANDRASEKHARAIAH, Hyperbolic thermoelasticity, A review of recent literature, Applied Mechanics Review, 51, 705-729, 1988.
• 11. A.N. SINHA, S.B. SINHA, Reflection of thermoelastic waves at a solid half-space with thermal relaxation, J. Phys. Earth, 22, 237-244, 1974.
• 12. S.B. SINHA, K.A. ELSIBAI, Reflection of thermoelastic waves at a solid half-space with two thermal relaxation times, J. Thermal Stresses, 19, 763-777, 1996.
• 13. S.B. SINHA, K.A. ELSIBAI, Reflection and refraction of thermoelastic waves at an interface of two semi-infinite media with two thermal relaxation times, J. Thermal Stresses, 20, 129-146, 1997.
• 14. A.N. ABD-ALLA, A.S. AL-DAWY, The reflection phenomena of SV waves in a generalized thermoelastic medium, Int. J. Math. Math. Sci., 23, 529-546, 2000.
• 15. J.N. SHARMA, V. KUMAR, D. CHAND, Reflection of generalized thermoelastic waves from the boundary of a half-space, J. Thermal Stresses, 26, 925-942, 2003.
• 16. L. KNOPOFF, The interaction between elastic wave motions and a magnetic field in electrical conductors, J. Geophys. Res., 60, 441-456, 1955.
• 17. P. CHADWICK, Elastic waves propagation in a magnetic field, [in:] Proceedings of the International Congress of Applied Mechanics, Brusseles, Belgium, 143-153, 1957.
• 18. S. KALISKI, J. PETYKIEWICZ, Equation of motion coupled with the field of temperature in a magnetic field involving mechanical and electrical relaxation for anisotropic bodies, Proc. Vibr. Probl., 4, 1-12, 1959.
• 19. A.N. ABD-ALLA, A.A. YAHIA, S.M. ABO-DAHAB, On reflection of the generalized rnagneto-thermo-viscoelastic plane waves, Chaos, Solitons & Fractals, 16, 211 231, 2003.
• 20. M.A. EZZAT, H.M. YOUSSEF, Generalized magneto-thermoelasticity in a perfectly conducting medium, International Journal of Solids and Structures, 42, 6319-6334, 2005.
• 21. A. BAKSI, R.K. BERA, L. DEBNATH, A study of magneto-thermoelastic problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium, International Journal of Engineering Science, 43, 1419 1434, 2005.
• 22. W. NOWACKI, Dynamical problems of thermoelastic diffusion in solids I, Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 55 64, 1974.
• 23. W. NOWACKI, Dynamical problems of thermoelastic diffusion in solids II, Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 129 135, 1974.
• 24. W. NOWACKI, Dynamical problems of thermoelastic diffusion in solids III, Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 266 274, 1974.
• 25. H.H. SHERIEF, F. HAMZA, H. SALEH, The theory of generalized thermoelastic diffusion, Int. J. Engrg. Sci., 42, 591 608, 2004.
• 26. B. SINGH, Reflection of P and SV waves from the free surface of an elastic solid with generalized thermodiffusion, J. Earth. Syst. Sci., 114, 2, 159 168, 2005.
• 27. B. SINGH, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration, 291, 764 778, 2006.
• 28. W.B. EWING, W.S. JARDETZKY, F. PRESS, Elastic Waves in Layered Media, McGraw-Hill, New York, p. 76, 1957.
• 29. A. BEN-MENHAMEN, S.J. SINGH, Seismic Waves and Sources, Springer, New York, pp. 89 95, 1981.