Reflection of Waves in a Rotating Transversely Isotropic Thermoelastic Half-space Under Initial Stress

Subject Areas : Engineering

R.R Gupta ¹ , R.R. Gupta ²

1 - Department of CS & IT Mazoon University College, Muscat, Oman
2 - Department of Mathematics, MEC, Muscat, Oman

Received: 2014-03-13 Accepted : 2014-05-10 Published : 2014-06-30

Keywords:

References:

[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.