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Computational and Applied Mathematics Journal

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Reflection and Refraction of Generalized Visco-Thermoelastic Waves at an Interface Between Two Half Spaces

Computational and Applied Mathematics Journal
Vol.2 , No. 1, Publication Date: Mar. 4, 2016, Page: 12-22

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Authors

[1]	Sutapa Santra, Department of Mathematics, Gargi Memorial Institute of Technology, Baruipur, Kolkata.
[2]	A. Lahiri, Department of Mathematics, Jadavpur University, Jadavpur, Kolkata.
[3]	N. C. Das, Department of Mathematics, Jadavpur University, Jadavpur, Kolkata.

Abstract

The reflection and refraction due to generalized thermoelastic incident P- and SV- waves at a plane interface between two dissimilar half spaces of visco-thermoelasitic materials have been investigated. Magnitude of coefficient ratios for both the cases of P- and SV- waves have been found out. Several graphs have been drawn to study the nature of variation of the amplitude ratios when the angle of incidence varies. Thermal and viscous effects are compared with the corresponding classical elastic cases.

Keywords

Reflection, Refraction, Visco-Thermoelastic Waves, P-Wave, SV-Wave

Reference

[01]	M. Biot, Thermoelasticity and Irreversible Thermodynamics, J. Appl. Phys., vol. 27, 240-253, 1956.
[02]	P. Chadwick, I. N. Sneddon, Plane Waves in an Elastic Solid Conducting Heat, J. Mech. Phys. Solids, vol. 6, 223-230, 1958.
[03]	W. Nowacki, Some Dynamic Problems of Thermoelasticity, Archiwum Mechaniki Stosowanej, vol. 11, No. 6, 737-750, 1959.
[04]	H. Parkus, Stress in a Centrally Heated Disc, Proc. 2^nd U. S. Nat. Congr. Appl. Mech., 307, 1954.
[05]	J. L. Nowinski, W. Olszak and W. Urbanowski, On the Thermoelastic Problem in the Case of Bodies of any type of Curvilinear Orthotropy, Archiwum Mechaniki Stosowanej, vol. 7, No. 2, 247-265, 1955.
[06]	A. D. Kovalenko, Thermoelasticity, Wolters Noordhoff, Groringen,1969.
[07]	B. A. Boley and J. H. Weiner, Theory of Thermal Stresses, John Wiley, N. Y., 1960.
[08]	I. N. Sneddon, Fourier Transforms, McGrawHill Book Company, inc. 1951.
[09]	G. Paria, Coupling of Elastic and Thermal Deformations, Appl. Sci. Res.: sec. a, 7, 463-475, 1959.
[10]	C. C. Acherman, B. Bentman, H. A. Fairbank and R. A. Guyer, Second Sound in Solid Helium, Phys. Rev. Lett., vol. 16, 789-791, 1966.
[11]	S. J. Rogers, Transport of Heat and Approach to Second Sound in Some Isotropically Pure Alkali-Halide Crystals, phys. Rev. b, 3, 1440-1457, 1971.
[12]	H. F. Jackson, C. T. Walker, Thermal Conductivity, Second Sound and Phonon-Phonon Interactions in NaF, Phys. Rev. b, 3, 1428-1439, 1971.
[13]	H. W. Lord and Y. Shulman, A Generalized Dynamic Theory of Thermoelasticity, J. Mech. Phys. Solids, vol. 15, 299-309, 1967.
[14]	A. E. Green and K. A. Lindsay, Thermoelasticity, Journal of Elasticity, vol. 2, 1-7, 1972.
[15]	A. E. Green and P. M. Naghdi, A Re-examination of the Basic Postulate of Thermomechanics, Proc, Roy soc., London Ser. A, vol. 432, 171-194, 1991.
[16]	A. E. Green and P. M. Naghdi, On Undamped Heat Waves in an Elastic Solid, J. Thermal stresses, vol. 15, No. 2, 253-264, 1992.
[17]	A. E. Green and P. M. Naghdi, Thermoelasticity without Energy Dissipation, J. Elasticity, vol. 31, 189-208, 1993.
[18]	S. B. Sinha, and K. A. Elsibai, Reflection and Refraction of Thermoelastic Waves at an Interface of Two Semi-infinite Media with Two Relaxation Time, J. Thermal stresses, vol. 20, 129-146, 1997.
[19]	J. N. Sharma, V. Kumar and Dayal Chand, Reflection of Generalized Thermoelastic Waves from the Boundary of a Half Space, J. of Thermal Stresses, 26: 10, 925-942, 2003, DOI: 10.1080/01495730306342.
[20]	J. Singh and S. K. Tomar, Plane Waves in a Rotating Generalized Thermoelastic Solid with Voids, Int. Jour. Engg. Sc. and Tech., vol. 3, No. 2, 34-41, 2011.
[21]	N. C. Das, A. Lahiri, S. Sarkar, and S. Basu, Reflection of Generalized Thermoelastic Waves from Isothermal and Insulated Boundaries of Half Space, J. Computers and Mathematics with Applications, vol. 56, 2795-2804, 2008.
[22]	A. Lahiri, N. C. Das, M. B. Bera and S. Basu, Reflection and Refraction of Generalized Temperature Rate Dependent Thermoelastic Waves at an Interface Between Two Semi-infinite Media, Int. J. of Applied Mechanics and Engineering, vol. 16, No. 4, 1051-1069, 2011.
[23]	A. I. Lavrentyev and S. I. Rokhlin, Anomalous Attenuation Effect on Reflectivity of an Ultrasonic Wave from a Thin Layer Between Dissimilar Materials, J. Acoust. Soc. Am., vol. 101, No. 6, 3405- 3414, 1997.
[24]	J. N. Sharma and Rattan Chand, Transient Thermoviscoelastic Waves in a Half – space due to Thermal Loads, Journal of Thermal Stresses, vol. 28, 233-252, 2005.
[25]	S. H. Mallik and M. Kanoria, Generalized Thermoelastic Functionally Graded Solid with a Periodically Varying Heat Source, International Journal of Solids and Structures, vol. 44, 7633-7645, 2007.