Share This Article:

Two and Three Dimensions of Generalized Thermoelastic Medium without Energy Dissipation under the Effect of Rotation

Abstract Full-Text HTML XML Download Download as PDF (Size:7864KB) PP. 793-805
DOI: 10.4236/am.2015.65075    3,000 Downloads   3,461 Views   Citations

ABSTRACT

The purpose of this paper is to study the effect of rotation on the general three-dimensional model of the equations of the generalized thermoelasticity for a homogeneous isotropic elastic half-space solid. The problem is studied in the context of the Green-Naghdi theory of type II (without energy dissipation). The normal mode analysis is used to obtain the expressions for the temperature, thermal stress, strain and displacement. The distributions of variables considered are represented graphically.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Othman, M. , Atwa, S. and Elwan, A. (2015) Two and Three Dimensions of Generalized Thermoelastic Medium without Energy Dissipation under the Effect of Rotation. Applied Mathematics, 6, 793-805. doi: 10.4236/am.2015.65075.

References

[1] Biot, M.A. (1956) Thermoelasticity and Irreversible Thermodynamics. Journal of Applied Physics, 27, 240-253.
http://dx.doi.org/10.1063/1.1722402
[2] Lord, H.W. and Shulman Y. (1967) A Generalized Dynamical Theory of Thermoelasticity. Journal of the Mechanics and Physics of Solids, 15, 299-309.
http://dx.doi.org/10.1016/0022-5096(67)90024-5
[3] Othman, M.I.A. (2002) Lord-Shulman Theory under the Dependence of the Modulus of Elasticity on the Reference Temperature in Two Dimensional Generalized Thermo-Elasticity. Journal of Thermal Stresses, 25, 1027-1045.
http://dx.doi.org/10.1080/01495730290074621
[4] Green, A.E. and Lindsay, K.A. (1972) Thermoelasticity. Journal of Elasticity, 2, 1-7.
http://dx.doi.org/10.1007/BF00045689
[5] Green, A.E. and Laws, N. (1972) On the Entropy Production Inequality. Archive for Rational Mechanics and Analysis, 45, 45-47.
http://dx.doi.org/10.1007/BF00253395
[6] Othman, M.I.A. (2004) Relaxation Effects on Thermal Shock Problems in an Elastic Half-Space of Generalized Magneto-Thermoelastic Waves. Mechanics and Mechanical Engineering, 7, 165-178.
[7] Green, A.E. and Naghdi, P.M. (1993) Thermoelasticity without Energy Dissipation. Journal of Elasticityy, 31, 189-208.
http://dx.doi.org/10.1007/BF00044969
[8] Chandrasekharaiah, D.S. (1986) Thermoelasticity with Second Sound: A Review. Applied Mechanics Reviews, 39, 354-376.
http://dx.doi.org/10.1115/1.3143705
[9] Chandrasekharaiah, D.S. (1998) Hyperbolic Thermoelasticity: A Review of Recent Literature. Applied Mechanics Reviews, 51, 705-729.
http://dx.doi.org/10.1115/1.3098984
[10] Tzou, D.Y. (1995) A Unified Approach for Heat Conduction from Macro- to Micro-Scales. Journal of Heat Transfer, 117, 8-16.
http://dx.doi.org/10.1115/1.2822329
[11] Tzou, D.Y. (1996) Macro to Micro-Scale Heat Transfer: The Lagging Behavior. Taylor and Francis, Washington DC.
[12] Hetnarski, R.B. and Ignaczak, J. (1998) Approaches to Generalized Thermoelasticity. Taormina Symposium, Italy, 1998, 25-40.
[13] Chand, D., Sharma, J.N. and Sud, S.P. (1990) Transient Generalized Magnetothermo-Elastic Waves in a Rotating Half Space. International Journal of Engineering Science, 28, 547-556.
http://dx.doi.org/10.1016/0020-7225(90)90057-P
[14] Schoenberg, M. and Censor, D. (1973) Elastic Waves in Rotating Media. Quarterly of Applied Mathematics, 31, 115-125.
[15] Clarke, N.S. and Burdness, J.S. (1994) Rayleigh Waves on a Rotating Surface. ASME Journal of Applied Mechanics, 61, 724-726.
http://dx.doi.org/10.1115/1.2901524
[16] Destrade, M. (2004) Surface Acoustic Waves in Rotating Orthorhombic Crystal. Proceedings of the Royal Society A, 460, 653-665.
http://dx.doi.org/10.1098/rspa.2003.1192
[17] Roychoudhuri, S.K. and Mukhopadhyay, S. (2000) Effect of Rotation and Relaxation Times on Plane Waves in Generalized Thermo-Visco-Elasticity. International Journal of Mathematics and Mathematical Sciences, 23, 497-505.
http://dx.doi.org/10.1155/S0161171200001356
[18] Ting, T.C.T. (2004) Surface Waves in a Rotating Anisotropic Elastic Half-Space. Wave Motion, 40, 329-346.
http://dx.doi.org/10.1016/j.wavemoti.2003.10.005
[19] Othman, M.I.A. and Song, Y. (2008) Effect of Rotation on Plane Waves of Generalized Electro-Magnetothermovis-coelasticity with Two Relaxation Times. Applied Mathematical Modelling, 32, 811-825.
http://dx.doi.org/10.1016/j.apm.2007.02.025
[20] Ailawalia, P. and Narah, N.S. (2009) Effect of Rotation in Generalized Thermoelastic Solid under the Influence of Gravity with an Overlying Infinite Thermoelastic Fluid. Applied Mathematics and Mechanics, 30, 1505-1518.
http://dx.doi.org/10.1007/s10483-009-1203-6
[21] Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2013) Effect of Magnetic Field and Rotation on Generalized Thermo-Microstretch. Elastic Solid with Mode-I Crack under the Green Naghdi Theory. Computational Mathematics and Modeling, 24, 566-591.
http://dx.doi.org/10.1007/s10598-013-9200-3
[22] Othman, M.I.A., Zidan, M.E.M. and Hilal, M.I.M. (2014) Effect of Magnetic Field on a Rotating Thermoelastic Medium with Voids under Thermal Loading Due to Laser Pulse with Energy Dissipation. Canadian Journal of Physics, 92, 1359-1371.
http://dx.doi.org/10.1139/cjp-2013-0689
[23] Othman, M.I.A. and Atwa, S.Y. (2014) Effect of Rotation on a Fiber-Reinforced Thermo-Elastic under Green-Naghdi Theory and Influence of Gravity. Meccanica, 49, 23-36.
http://dx.doi.org/10.1007/s11012-013-9748-1

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.