Wave propagation in generalized thermodiffusion elastic medium with impedence boundary condition. (English) Zbl 1503.74061
Summary: In the present investigation, we study the reflection of plane waves, that is, Longitudinal displacement wave (P-Wave), Thermal wave (T-Wave) and Mass Diffusive wave (MD-Wave) in thermodiffusion elastic-half medium which is subjected to impedence boundary condition in context of one relaxatioon time theory given by Lord and Shulman theory (L-S) and the Coupled theory (C-T) of thermoelasticity. The expressions of amplitude ratios are obtained numerically and their variation with angle of incidence is presented graphically for a particular model to emphasize on the impact of impedence parameter, relaxation time and diffusion. Some special cases are also deduced.
Keywords:
mass diffusive wave; amplitude ratio; plane wave; wave reflection; one-relaxation time theory; Lord-Shulman thermoelasticityReferences:
| [1] | W. Nowacki, Dynamical Problems of Thermo Diffusion in Solids I , Bull Acad. Pol. Sci. Ser. Sci, tech, 22, (1974)(a), 55-64. |
| [2] | W. Nowacki, Dynamical Problems of Thermo Diffusion in Solids II, Bull Acad. Pol. Sci. Ser. Sci, tech, 22, (1974)(b), 129-135. |
| [3] | W. Nowacki, Dynamical Problems of Thermo Diffusion in Solids III, Bull Acad. Pol. Sci. Ser. Sci, tech, 22, (1974)(c), 257-266. |
| [4] | W. Nowacki, Dynamical Problems of Thermo Diffusion in Solids, Engg. Frac. Mech, 8, (1976), 261-266. · Zbl 0354.73009 |
| [5] | B. Singh, Reflection of P and SV Waves from Free Surface of an Elastic Soild with Generalized Thermodiffusion, J. Earth Syst. Sci, 114 (2), (2005), 159-168. |
| [6] | B. Singh, Reflection of SV Waves from Free Surface of an Elastic Solid with Generalized Thermoelastic Diffusion, J. sound vib., 291, (3-5), (2006), 764-778. · Zbl 1243.74025 |
| [7] | M. Aouadi, Uniqueness and Reciprocity Theorems in the Theory of Generalized Ther-moelastic Diffusion, Journal of Thermal Stresses, 30, (2007), 665-678. |
| [8] | M. Aouadi, A Problem for an Infinite Elastic Body with a Spherical Cavity in the Theory of Generalized Thermoelastic Diffusion, International Journal of Solids and Structures, 44, (2007), 5711-5722. · Zbl 1126.74013 |
| [9] | J. N. Sharma, Y. D. Sharma, P. K. Sharma, On the Propagation Elasto-thermodiffusive Surface Waves in Heat-conducting Materials, Journal of Sound and Vibration, 315(4), (2008), 927-938. |
| [10] | S. M. Abo-Dahab, B. Singh, Influences of Magnetic Field on Wave Propagation in Gener-alized Thermoelastic Solid with Diffusion, Archives of Mechanics, 61(2), (2009), 121-136. · Zbl 1273.74146 |
| [11] | R. Kumar, M. Panchal, A Study of Axi-symmetric Waves Through an Isotropic Ther-moelastic Diffusive Medium, Computational and Applied Mathematics, 30(2),(2011), 247-265. · Zbl 1261.74018 |
| [12] | R. Kumar, T. Kansal, Plane Waves and Fundamental Solution in the Generalized The-ories of Thermoelastic Diffusion, IJAMM, 8(4), (2012), 21-34. |
| [13] | H. F. Tiersten, Elastic Surface Waves Guided by Thin Films, Journal of Applied Physics, 40, (1969), 770-789. |
| [14] | P. G. Malischewsky, Surface Waves and Discontinuities, Elsevier, Amsterdam 1987. |
| [15] | P. C. Vinh, T. T. Hue, Rayleigh Waves with Impedance Boundary Conditions in Anisotropic Solids, Wave Motion, 51, (2014), 1082-1092. · Zbl 1456.74084 |
| [16] | B. Singh B, Reflection of Elastic Waves from Plane Surface of a Half-space with Impedance Boundary Conditions, Geosciences Research, 2(4), (2017), 242-253. |
| [17] | B. Singh , A. Kumar, S. Kaushal, Effect of Impedance Boundary on Reflection of Plane Waves from Free Surface of Rotating Thermoelastic Solid Half Space, Research Journal of Engineering, 8(4), (2017), 405-413. |
| [18] | H. Sherief, F. Hamza, H. Saleh, The Theory of Generalized Thermoelastic Diffusion, Int. Journal Eng. Sci, 42, (2004), 591-608. · Zbl 1211.74080 |
| [19] | A. C. Schoenberg, Transmission and Reflection of Plane Waves at an Elastic-viscoelastic Interface, Geophysics J.R. Astr. Soc., 25, 35-47. · Zbl 0246.73033 |
| [20] | H. Sherief , H. Saleh, A Half Space Problem in the Theory of Generalized Thermoelastic Diffusion, Int. Journal of Solids structures, 42, (2005), 4484-4493. · Zbl 1119.74366 |
| [21] | L. Thomas, Fundamental of Heat Transfer, Prentice hall Inc-Englewmd Diffs, Newjersey, 1980. [ DOI: 10. · Zbl 1503.74061 · doi:10.52547/ijmsi.17.2.1 |
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