Reflection of Waves in a Rotating Transversely Isotropic Thermoelastic Half-space Under Initial Stress
الموضوعات :
1 - Department of CS & IT Mazoon University College, Muscat, Oman
2 - Department of Mathematics, MEC, Muscat, Oman
الکلمات المفتاحية: Amplitude ratios, Rotation, Initial stress, Thermoelasticity, Reflection, Plane wave,
ملخص المقالة :
The present paper concerns with the effect of initial stress on the propagation of plane waves in a rotating transversely isotropic medium in the context of thermoelasticity theory of GN theory of type-II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasi-longitudinal wave. The slowest of them is a thermal wave. The remaining is called quasi-transverse wave. The prefix ‘quasi’ refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically, simulated results have been plotted graphically with respect to frequency to evince the effect of initial stress and anisotropy.
[1] Biot M. A., 1965, Mechanics of Incremental Deformations, John Wiley, New York.
[2] Chandrasekhariah D. S., 1998, Hyperbolic thermoelasticity: a review of recent literature, Applied Mechanics Reviews 51:705-729.
[3] Chandrasekharaiah D. S., Srinath K. S., 1996, One-dimensional waves in a thermo- elastic half-space without energy dissipation, International Journal of Engineering Science 34:1447-1455.
[4] Chandrasekharaiah D. S., Srinath K. S., 1997, Axisymmetric thermoelastic inter- actions without energy dissipation in an unbounded body with cylindrical cavity, Journal of Elasticity 46:19-31.
[5] Chand D., Sharma J.N., Sud S.P., 1990, Transient generalized magneto-thermoelastic waves in a rotating half space, International Journal of Engineering Science 28:547-556.
[6] Chattopadhyay A., Bose S., Chakraborty M., 1982, Reflection of elastic waves under initial stress at a free surface, Journal of Acoustical Society of America 72: 255-263.
[7] Clarke N.S., Burdness J.S., 1994, Rayleigh waves on a rotating surface, Journal of Applied Mechanics,Transactions of ASME 61:724-726.
[8] Destrade M., 2004, Surface waves in rotating rhombic crystal, Proceeding of the Royal Society A 460 :653-665.
[9] Dey S., Roy N., Dutta A., 1985, Reflection and refraction of p-waves under initial stresses at an interface, Indian Journal of Pure and Applied Mathematics16:1051-1071.
[10] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
[11] Green A.E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2:1-5.
[12] Green A.E., Naghdi P.M., 1991, A re-examination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London Series A 432:171-194.
[13] Green A.E., Naghdi P. M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15:253-264.
[14] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31:189-208.
[15] Gupta R. R., 2011, Propagation of waves in the transversely isotropic thermoelastic Green and Naghdi type-II and type-III medium, Journal of Applied Mechanics and Technical Physics 52(5):825-833.
[16] Gupta R.R.,2013, Reflection of waves in visco-thermoelastic transversely isotropic medium, International Journal for Computational Methods in Engineering Science and Mechanics 14: 83-89.
[17] Gupta R. R., Gupta R. R., 2013, Analysis of wave motion in an initially stressed anisotropic fiber-reinforced thermoelastic medium, Earthquakes and Structures 4(1):1-10.
[18] Gupta R. R., Gupta R. R., 2013, Reflection of waves in initially stressed transversely isotropic fibre-reinforced thermoelastic medium, International Journal of Advances in Management and Economics 18(3): 671-685.
[19] Hetnarski R.B., Iganazack J., 1999, Generalised thermoelasticity, Journal of Thermal Stresses 22:451-470.
[20] Lord H., Shulman Y.A., 1967, Generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[21] Mahmoud S. R., 2011, Effect of rotation, gravity field and initial stress on generalized magneto-thermoelastic rayleigh waves in a granular medium, Applied Mathematical Sciences 5(41):2013-2032.
[22] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial stress, Journal of Acoustical Society of America 106:1586–1588.
[23] 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 of Solids and Structures 44:5651-5664.
[24] Othman M.I.A., 2008, Effect of rotation on plane waves in generalized thermoelasticity with two relaxation times, International Journal of Solids and Structures 41:2939-2956.
[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 of Solids and Structures 44:5651-5664.
[26] Othman M.I.A., Song Y., 2008, Reflection of magneto-thermo elastic waves from a rotating elastic half-space, International Journal of Engineering Sciences 46:459-474.
[27] Othman M.I.A., Song Y., 2009, The effect of rotation on 2-d thermal shock problems for a generalized magneto-thermo-elasticity half-space under three theories, Multidiscipline Modeling in Mathematics and Structures 5:43-58.
[28] Schoenberg M., Censor D., 1973, Elastic waves in rotating media, Quarterly of Applied Mathematics 31:115-125.
[29] Sharma J.N., 2007, Effect of rotation on rayleigh-lamb waves in piezothermoelastic half space, International Journal of Solids and Structures 44:1060-1072.
[30] Sidhu R.S., Singh S.J., 1983, Comments on “reflection of elastic waves under initial stress at a free surface”, Journal of Acoustical Society of America 74:1640-1642.
[31] Singh B., 2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Journal of Applied Mathematics and Computation 198:494-505.
[32] Singh B. B., Kumar A., Singh J., 2006, Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress, Journal of Applied Mathematics and Computation 177:170-177.
[33] Slaughter W. S., 2002, The Linearized Theory of Elasticity, Birkhauser.
