On generalized magneto-thermoelastic P-, T- and SV-waves propagation at the interface between two magnetized solid-liquid media with initial stress

• Autorzy: Abo-Dahab S. M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the effects of magnetic field and initial stress on plane waves propagation. We have investigated the problem of reflection and refraction of thermoelastic waves at a magnetized solid-liquid interface in the presence of initial stress, in the context of CT (Classical theory) of thermoelasticity, the problem has been solved. The boundary conditions applied at the interface are: (i) continuity of the displacement, (ii) vanishing of the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) vanishing of the tangential stress and (v) continuity of temperature. The amplitudes ratios for the incident P-, T-, and SV- waves have been obtained. The reflection and transmission coefficients for the incident waves are computed numerically, considering the initial stress and magnetic field effects and the results are represented graphically.

Słowa kluczowe

EN

initial stress; CT theory; rotating frame; reflection; refraction; thermoelasticity

PL

naprężenia pierwotne; teoria klasyczna; rama obrotowa; odbicie; refrakcja; termoelastyczność

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. 21, nr 4
• Strony: 897--917
• Opis fizyczny: Bibliogr. 35 poz., rys., wykr.

Twórcy

autor

Abo-Dahab S. M.

• Math. Dept., Faculty of Science, South Valley University, Qena 83523, Egypt
• Math. Dept., Faculty of Science, Taif University 888, Saudi Arabia

Bibliografia

• [1] Danilovskaya, V.: Thermal stresses in an elastic half-space due to sudden heating of its boundary, Prikl Mat. Mekh., 14, 316-324, 1950.
• [2] Biot, M. A.: Mechanics of Incremental Deformations, John Wiley and Sons, Inc., New York, 1965.
• [3] Lord, H. W. and Shulman, Y.: A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299-309, 1967.
• [4] Green, A. E. and Lindsay, K. A.: Thermoelasticity, J. Elasticity, 2, 1-7, 1972.
• [5] Green, A. E. and Naghdi, P. M.: A re-examination of the basic postulates of thermo-mechanics, P. Roy. Soc. Lond., A 432, 171-194, 1991.
• [6] Green, A. E. and Naghdi, P. M.: On undamped heat waves in an elastic solid, J. Therm. Stresses, 15, 253-264, 1992.
• [7] Green, A. E. and Naghdi, P. M.: Thermoelasticity without energy dissipation, J. Elasticity, 31, 189-208, 1993.
• [8] Chandrasekharaiah, D. S.: Hyperbolic thermoelasticity: a review of recent literature, Appl. Mech. Rev., 51, 12, 705-729, 1998.
• [9] Sinha, S. B. and Elsibai, K. A.: Reflection of thermoelastic waves at a solid half-space with two relaxation times, J. Therm. Stress., 19, 763-777, 1996.
• [10] Abd-alla, A. N. and Al-Dawy, A. A. S.: The Reflection phenomena of SV waves in a generalized thermoelastic medium, Int. J. Math. Math. Sci., 23, 8, 529-540, 2000.
• [11] Abd-alla, A. N., Yahia, A. A. and Abo-Dahab, S. M.: On the reflection of the generalized magneto-thermo-viscoelastic plane waves, Chaos, Solitons & Fractals, 16, 2, 211-231, 2003.
• [12] Sinha, A. B. and Elsibai, K. A.: Reflection and refraction of thermoelastic waves at an interface of two semi-Infinite media with two thermal relaxation times, J. Therm. Stress., 20, 2, 129-146, 1997.
• [13] Hetnarski, R. B. and Ignaczak, J.: Generalized thermoelasticity, J. Therm. Stress., 22, 451-476, 1999.
• [14] Singh, B.: Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch, Sadhana 25, 6, 589-600, 2000.
• [15] Kumar, R. and Sarathi, P.: Reflection and refraction of thermoelastic plane waves at an interface between two thermoelastic media without energydissipation, Arch. Mech., 58, 1, 155-185, 2006.
• [16] Othman, M. I. A. and Song, Y.: Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation, Int. J. Solids Struct., 44, 5651-5664, 2007.
• [17] Abd-Alla, A. N. and Abo-Dahab, S. M.: The influence of the viscosity and the magnetic field on reflection and transmission of waves at interface between magnetoviscoelastic materials, Meccanica, 43, 437-448, 2008.
• [18] Othman, M. I. A and Song, Y.: Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli, Appl. Math. Model., 32, 483-500, 2008.
• [19] Abo-Dahab, S. M. and Singh, B.: Influences of magnetic field on wave propagation in generalized thermoelastic solid with diffusion, Arch. Mech., 61, 121-136, 2009.
• [20] Abo-Dahab, S. M. and Mohamed, R. A.: Influence of magnetic field and hydrostatic initial stress on reflection phenomena of P and SV waves from a generalized thermoelastic solid half-space, J. Vib. & Control, 16, 685-699, 2010.
• [21] Abo-Dahab, S. M., Mohamed, R. A. and Singh, B.: Rotation and magnetic field effects on P wave reflection from stress-free surface elastic half-space with voids under one thermal relaxation time, J. Vib. & Control, 17, 12, 1827-1839, 2011.
• [22] Abo-Dahab, S. M.: Reflection of P and SV waves from stress-free surface elastic half-space under influence of magnetic field and hydrostatic initial stress without energy dissipation, J. Vib. & Control, 17, 14, 2213-2221, 2011.
• [23] Abo-Dahab, S. M., Mohamed, R. A. and Abd-Alla, A.M.: Effect of relaxation times and magnetic field on the reflection of thermoelastic waves from isothermal and insulated boundaries of a half space, Int. Review of Physics, 5, 5, 247-258, 2011.
• [24] Abo-Dahab, S. M., and Asad, A. J.: Maxwell’s stresses effect on reflection and transmission of plane waves between two thermo-elastic media under GN Model, Int. Review of Physics, 5, 5, 286-299, 2011.
• [25] Deswal, S., Singh, L. and Singh, B.: Reflection and refraction at an interface between two dissimilar thermally conducting viscous liquid half-spaces, International Journal of Pure and Applied Mathematics, 70, 6, 807-824, 2011.
• [26] Chakraborty, N. and Singh, M. C.: Reflection and refraction of a plane thermoelastic wave at a solid-solid interface under perfect boundary condition, inpresence of normal initial stress, Appl. Math. Model., 35, 11, 5286-5301, 2011.
• [27] Abd-Alla, A. M., Mahmoud, S. R. and Abo-Dahab, S. M.: On problem of transient coupled thermoelasticity of an annular fin, Meccanica, 47, 1295-1306, 2012.
• [28] Abo-Dahab, S. M. and Singh, B.: Rotational and voids effects on the reflection of P waves from stress-free surface of an elastic half-space under magnetic field, initial Stress and without energy dissipation, Appl. Math. Model., 37, 8999-9011, 2013.
• [29] Singh, M. C. and Chakraborty, N.: Reflection and refraction of P-, SV- and thermal waves, at an initially stressed solid-liquid interface in generalized thermoelasticity, Appl. Math. Model., 37, 463-475, 2013.
• [30] Abo-Dahab, S. M. and Salama, M. M.: A plane magneto-thermoelastic waves reflection and refraction between two solid media with external heat sources and initial stress, J. Therm. Stress., 37, 1124-1151, 2014.
• [31] Abd-Alla, A. M., Abo-Dahab, S. M. and El-Semiry, R. D.: Effect of rotation on peristaltic flow of a micropolar fluid through a porous medium with an external magnetic field, Journal of Magnetism and Magnetic Materials, 348, 33- 43, 2013.
• [32] Abd-Alla, A. M., Abo-Dahab, S. M. and El-Shahrany, H. D.: Effects of rotation and initial stress on peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field, Journal of Magnetism and Magnetic Materials, 349, 268-280, 2014.
• [33] Cho, E. and Gurnis, M.: Thermally induced brittle deformation in oceanic lithosphere and the spacing of fracture zones, Earth Planet. Sci. Lett., 269, 1-2, 259-270, 2008.
• [34] Song, Y., Xu, H. and Zhang, Y.: Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media, International Journal of Thermophysics, 27, 3, 970-993, 2006.
• [35] Nayfeh, A. and Nasser, S. N.: Thermoelastic waves in solids with thermal relaxation, Acta Mech. 12, 53-69, 1971.