Kumar, R., Garg, S., Ahuja, S. (2015). Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface. Journal of Solid Mechanics, 7(2), 223-238.

R Kumar; S.K Garg; S Ahuja. "Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface". Journal of Solid Mechanics, 7, 2, 2015, 223-238.

Kumar, R., Garg, S., Ahuja, S. (2015). 'Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface', Journal of Solid Mechanics, 7(2), pp. 223-238.

Kumar, R., Garg, S., Ahuja, S. Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface. Journal of Solid Mechanics, 2015; 7(2): 223-238.

Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface

^{1}Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India

^{2}Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana,India

^{3}University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana, India

Abstract

The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves with incidence of quasi-longitudinal (qP), quasi-thermal (qT) & quasi- transverse (qSV) waves respectively at an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance and welded boundaries.The reflection and transmission coefficients are functions of frequency, initial stress and angle of incidence. There amplitude ratios are computed numerically and depicted graphically for a specific model to show the effect of initial stress. Some special cases are also deduced from the present investigation.

[1] Spencer A.J.M., 1941, Deformation of Fibre-Reinforced Materials, Clarendon Press, Oxford. [2] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15(5):299-309. [3] Green A.E., Lindsay K.A.,1971, Thermoelasticity, Journal of Elasticity 2(1):1-7. [4] Dhaliwal R.S., Sherief H.H.,1980, Generalized thermoelasticity for anisotropic media, The Quarterly of Applied Mathematics 33(1):1-8. [5] Erdem A.U., 1995, Heat Conduction in fiber-reinforced rigid bodies, 10 Ulusal Ist Bilimi ve Tekmgi Kongrest, 6-8 Eylul, Ankara. [6] Kumar R., Rani R., 2010, Study of wave motion in an anisotropic fibre-reinforced thermoelastic solid, Journal of Solid Mechanics 2(1):91-100. [7] Deresiewicz H., 1960, Effect of boundaries on waves in a thermoelastic solid, Journal of the Mechanics and Physics of Solids 8(3):164-172. [8] Sinha A.N., Sinha S.B., 1974, Reflection of thermoelastic waves at a solid half-space with thermal relaxation, Journal of Physics of the Earth 22(2):237-244. [9] Sinha S.B., Elsibai K.A.,1966, Reflection of thermoelastic waves at a solid half-space with two relaxation times, Journal of Thermal Stresses 19(8):763-777. [10] Sinha S.B., Elsibai K.A., 1997, Reflection and transmission of thermoelastic waves at an interface of two semi-infinite media with two relaxation times, Journal of Thermal Stresses 20(2):129-146. [11] Singh B., 2002, Reflection of thermo-viscoelastic waves from free surface in the presence of magnetic field, Proceedings of the National Academy of Sciences, India,72A II,109-120. [12] Abd-Alla A.N., Yahia A.A., Abo-Dabah S.M., 2003, On reflection of the generalized magneto-thermo-viscoelastic plane waves, Chaos, Solitons Fractals 16(2):211-231. [13] Singh B., 2006, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration 291(3-5):764-778. [14] Song Y.Q., Zhang Y.C., Xu H.Y., Lu B.H.,2006, Magneto-thermoelastic wave propagation at the interface between two micropolar viscoelastic media, Applied Mathematics and Computation 176 (2):785-802. [15] Singh S., Khurana S., 2001, Reflection and transmission of P and SV waves at the interface between two monoclinic elastic half-spaces, Proceedings of the National Academy of Sciences, India ,71(A) IV. [16] Kumar R., Singh M., 2008, Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half space, Materials Science and Engineering 472(1-2):83-96. [17] Biot M.A., 1965, Mechanics of Incremental Deformations, John Wiley and Sons, New York. [18] Chattopadhyay A., Bose S., Chakraborty M., 1982, Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 72(1):255-263. [19] Sidhu R.S., Singh S.J., 1983, Comments on “Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 74(5):1640-1642. [20] Dey S., Roy N., Dutta A.,1985, Reflection and transmission of P-waves under initial stresses at an interface, Indian Journal of Pure and Applied Mathematics 16:1051-1071. [21] Selim M.M., 2008, Reflection of plane waves at free surface of an initially stressed dissipative medium, Proceedings of World Academy of Sciences, Engineering and Technology. [22] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial stress, The Journal of the Acoustical Society of America 106(31):1586-1588. [23] Singh B., Kumar A., Singh J.,2006, Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress, Applied Mathematics and Computation 177(1):170-177. [24] Singh B.,2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Applied Mathematics and Computation 198(2):494-505. [25] Othman M.I.A., Song Y., 2007, Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation, International Journal Solids and Structures 44 (17):5651-5664. [26] Abd-Alla A.El.N., Alsheikh F.A., 2009, The effect of the initial stresses on the reflection and transmission of plane quasi-vertical transverse waves in piezoelectric materials, World Academy of Science, Engineering and Technology 3. [27] Chattopadhyay A., Venkateswarlu R.L.K., Chattopadhyay A., 2007, Reflection and transmission of quasi P and SV waves at the interface of fibre-reinforced media, Advanced Studies in Theoretical Physics 1(2):57-73. [28] Abbas I.A., Othman M.I.A., 2012, Generalized thermoelastic interaction in a fibre-reinforced anisotropic half-space under hydrostatic initial stress, Journal of Vibration and Control 18(2):175-182 [29] Singh S. S. and Zorammuana C., 2013, Incident longitudinal wave at a fibre-reinforced thermoelastic half-space, Journal of Vibration and Control 20(12):1895-1906.