Wave Propagation in Mixture of Generalized Thermoelastic Solids Half-Space

Journal of Solid Mechanics

مقاله 1، دوره 2، شماره 3، آذر 2010، صفحه 199-213   

نوع مقاله: Research Paper

نویسندگان

R Kumar^{* 1}؛ S Devi²

¹Department of Mathematics, Kurukshetra University

²Department of Mathematics, D.N. College

چکیده

This paper concentrates on the reflection of plane waves in the mixture of generalized thermo elastic solid half-space. There exists quasi dilatational waves i.e. qP₁, qP₂, qT and two rotational waves S₁, S₂ in a two dimensional model of the solid. The boundary conditions are solved to obtain a system of five non-homogeneous equations for amplitude ratios. These amplitude ratios are found to depend on the angle of incidence of incident wave, mixture and thermal parameters and have been computed numerically and presented graphically. The appreciable effects of mixtures and thermal on the amplitude ratios are obtained.

کلیدواژه‌ها

Dynamic theory of mixture؛ Amplitude ratios؛ Thermoelasticity؛ Wave propagation؛ Relaxation time؛ Reflection

مراجع

[1] Trusedell C., Tupin R.A., 1960, The Classical Field Theories, Volume III/1, Springer-Verlag, Berlin.

[2] Eringen A.C., Ingram J.D., 1965, A continuum theory of chemically reacting media-I, International Journal of Engineering Science 3: 197-212.

[3] Green A.E., Naghdi P.M., 1965, A dynamical theory of interacting continua, International Journal of Engineering Science 3: 231-241.

[4] Bedford A., Stern M., 1972, A multi-continuum theory of elastic materials, Acta Mechanica 14: 85-102.

[5] Bedford A., Stern M., 1972, Toward a diffusing continuum theory of composite elastic materials, ASME Journal of Applied Mechanics 38: 8-14.

[6] Bowen R.M., 1976, Theory of mixtures, in: Continuum Physics, Volume III, edited by A.C. Eringen, Academic Press, New York.

[7] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Applications, Journal of the Institute of Mathematical Applications 17: 153-207.

[8] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Basic theory and Historical Development, Quarterly Journal of Mechanics and Applied Mathematics 29: 209-245.

[9] Rajgopal K.R., Tao L., 1995, Mechanics of Mixtures, World Scientific, Singapore.

[10] Iesan D., 1991, On the theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 14: 389-408.

[11] Green A.E., Steel T.R., 1966, Constitutive equations for intereacting continua, International Journal of Engineering Science 4: 483-500.

[12] Steel T.R., 1967, Applications of theory of interacting continua, Quarterly Journal of Mechanics and Applied Mathematics 20: 57-72.

[13] Bowen R.M., Wiese J.C., 1969, Diffusion in mixtures of elastic materials, International Journal of Engineering Science 7: 689-722.

[14] Martinez F., Quintanilla R., 1995, Some qualitative results for the linear theory of binary mixtures of thermoelastic solids, Collectanea Mathematica 46: 263-277.

[15] Pompei A. Scalia A., 1999, On the theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 22: 23-34.

[16] Burchuladze T., Svanadze M., 2000, Potential method in the linear theory of binary mixtures of thermoelastic solids, Journal of Thermal Stresses 23: 601-626.

[17] Pompei A., 2003, On the dynamical theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 26: 873-888.

[18] Passarella F., Vittorio Z., 2007, Some exponential decay estimates for the thermoelastic mixtures, Journal of Thermal Stresses 30: 25-41.

[19] Sharma M. D., Gogna M. L., 1992, Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid, Pageoph 138: 249-266.

[20] Vashisth A. K., Sharma M. D., Gogna M. L., 1991, Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solids, Geophysics International Journal 105: 601-617.

[21] Apice C.D., Chirita S., Tibullo V., 2005, On the spatial behavior in dynamic theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 28: 63-82.

[22] Lord H., Shulman Y.A., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.

[23] Schoenberg M., 1971, Transmission and reflection of plane waves at an elastic-viscoelastic interface, Geophysical Journal Royal Astronomical Society 25:35-47.

[24] Dhaliwal R. S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publishers, Delhi.