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A Two-Dimensional Problem for a Rotating Magneto-Thermoelastic Half-Space with Voids and Gravity in a Two-Temperature Generalized Thermoelasticity Theory

Published online by Cambridge University Press:  15 July 2015

S. Deswal  and
N. Hooda
S. Deswal
Affiliation:
Department of Mathematics, Guru Jambheshwar University of Science and Technology, Haryana, India
N. Hooda*
Affiliation:
Department of Mathematics, Guru Jambheshwar University of Science and Technology, Haryana, India
*
*Corresponding author ([email protected])
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Abstract

The present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

Keywords

Two-temperatureGeneralized thermoelasticityVoidsNormal mode analysis
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 639 - 651
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

REFERENCES

1.Lord, H. W. and Shulman, Y., “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, 15, pp. 299–309 (1967).Google Scholar
2.Green, A. E. and Lindsay, K. A., “Thermoelasticity,” Journal of Elasticity, 2, pp. 1–7 (1972).CrossRefGoogle Scholar
3.Hetnarski, R. B. and Ignaczak, J., “Generalized Thermoelasticity,” Journal of Thermal Stresses, 22, pp. 451–476 (1999).Google Scholar
4.Goodman, M. A. and Cowin, S. C., “A Continuum Theory for Granular Material,” Archive for Rational Mechanics and Analysis, 44, pp. 248–265 (1972).CrossRefGoogle Scholar
5.Nunziato, J. W. and Cowin, S. C., “A Non-Linear Theory of Elastic Materials with Voids,” Archive for Rational Mechanics and Analysis, 12, pp. 175–201 (1979).Google Scholar
6.Cowin, S. C. and Nunziato, J. W., “Linear Theory of Elastic Materials with Voids,” Journal of Elasticity, 13, pp. 125–147 (1983).CrossRefGoogle Scholar
7.Iesan, D., “A Theory of Thermoelastic Materials with Voids,” Acta Mechanica, 60, pp. 67–89 (1986).CrossRefGoogle Scholar
8.Tomar, S. K., “Elastic Wave Propagation in Materials with Voids-A Review,” The Mathematics Student, 76, pp. 241–260 (2007).Google Scholar
9.Dhaliwal, R. S. and Wang, J., “Domain of Influence Theorem in the Theory of Elastic Materials with Voids,” International Journal of Engineering Science, 32, pp. 1823–1828 (1994).Google Scholar
10.Dhaliwal, R. S. and Wang, J., “A Heat-Flux Dependent Theory of Thermoelasticity with Voids,” Acta Mechanica, 110, pp. 33–39 (1995).Google Scholar
11.Gurtin, M. E. and Williams, W. O., “On the Clausi-us-Duhem Inequality,” Zeitschrift für angewandte Mathematik und Physik, 17, pp. 626–633 (1966).Google Scholar
12.Gurtin, M. E. and Williams, W. O., “An Axiomatic Foundation for Continuum Thermodynamics,” Archive for Rational Mechanics and Analysis, 26, pp. 83–117 (1967).Google Scholar
13.Chen, P. J. and Gurtin, M. E., “On a Theory of Heat Conduction Involving Two Temperatures,” Zeitschrift für angewandte Mathematik und Physik, 19, pp. 614–627 (1968).Google Scholar
14.Chen, P. J., Gurtin, M. E. and Williams, W. O., “A Note on Non-Simple Heat Conduction,” Zeitschrift für Angewandte Mathematik Und Physik, 19, pp. 969–970 (1968).Google Scholar
15.Chen, P. J., Gurtin, M. E. and Williams, W. O., “On the Thermodynamics of Non-Simple Elastic Materials with Two Temperatures,” Zeitschrift für angewandte Mathematik und Physik, 20, pp. 107–112 (1969).Google Scholar
16.Bassiouny, E. and Youssef, H. M., “Two-temperature Generalized Thermopiezoelasticity of Finite Rod Subjected to Different Types of Thermal Loading,” Journal of Thermal Stresses, 31, pp. 1–13 (2008).Google Scholar
17.Youssef, H. M., “Two-Temperature Generalized Thermoelastic Infinite Medium with Cylindrical Cavity Subjected to Moving Heat Source,” Archive of Applied Mechanics, 80, pp. 1213–1224 (2010).CrossRefGoogle Scholar
18.Kaushal, S., Kumar, R. and Miglani, A., “Response of Frequency Domain in Generalized Thermoelastic-ity with Two Temperatures,” Journal of Engineering Physics and Thermophysics, 83, pp. 1080–1088 (2010).Google Scholar
19.Ezzat, M., Hamza, F. and Awad, E., “Electro-Magneto-Thermoelastic Plane Waves in Micropolar Solid Involving Two Temperatures,” Acta Mechanica Solida Sinica, 23, pp. 200–212 (2010).Google Scholar
20.Ezzat, M. A. and El-Karamany, A. S., “Two-Temperature Theory in Generalized Magneto-Thermoelasticity with Two Relaxation Times,” Meccanica, 46, pp. 785–794 (2010).CrossRefGoogle Scholar
21.Banik, S. and Kanoria, M., “Effects of Three-Phase-Lag on Two-Temperature Generalized Thermoelasticity for Infinite Medium with Spherical Cavity,” Applied Mathematics and Mechanics, 33, pp. 483–498 (2012).Google Scholar
22.Bromwich, T. J. J. A., “On the Influence of Gravity on Elastic Waves and in Particular on the Vibrations of an Elastic Globe,” Proceedings of the London Mathematical Society, 30, pp. 98–120 (1898).Google Scholar
23.Ahmed, S. M., “Influence of Gravity Field on the Propagation of Waves in Granular Medium,” International Journal of Mathematics and Mathematical Sciences, 23, pp. 627–637 (2000).Google Scholar
24.Abd-Alla, A. M. and Ahmed, S. M., “Rayleigh Waves in an Orthotropic Thermoelastic Medium under Gravity and Initial Stress,” Earth Moon Planets, 75, pp. 185–197 (1998).Google Scholar
25.Mahmoud, S. R., “Influence of Rotation and Generalized Magneto-Thermoelastic on Rayleigh Waves in a Granular Medium under Effect of Initial Stress and Gravity Field,” Meccanica, 47, pp. 1561–1579 (2012).Google Scholar
26.Roy-Choudhury, S. K. and Mukhopdhyay, S., “Effect of Rotation and Relaxation on Plane Waves in Generalized Thermo-Viscoelasticity,” International Journal of Mathematics and Mathematical Sciences, 23, pp. 497–505 (2000).Google Scholar
27.Ailawalia, P. and Narah, N. S., Effect of Rotation in Generalized Thermoelastic Solid under the Influence of Gravity with an Overlying Infinite Thermoelastic Fluid,” Journal of Applied Mathematics and Mechanics, 30, pp. 1505–1518 (2009).Google Scholar
28.Abd-Alla, A. M., Abo-Dahab, S. M., Hammad, H. A. and Mahmoud, S. R., “On Generalized Magneto-Thermoelastic Rayleigh Waves in a Granular Medium under Influence of Gravity Field and Initial stress,” Journal of Vibration and Control, 17, pp. 115–128 (2011).Google Scholar
29.Abd-Alla, A. M. and Mahmoud, S. R., “Magneto-Thermoelastic Problem in Rotating Non-Homogeneous Orthotropic Hollow Cylinder under the Hyperbolic Heat Conduction Model,” Meccanica, 45, pp. 451–462 (2010).Google Scholar
30.Othman, M. I. A. and Song, Y., “The Effect of Rotation on the Reflection of Magneto-Thermoelastic Waves under Thermoelasticity without Energy Dissipation,” Acta Mechanica, 184, pp. 189–204 (2007).CrossRefGoogle Scholar
31.Sherief, H. and Helmy, K., “A Two-Dimensional Problem for a Half-Space in Magneto- Thermoelas-ticity with Thermal Relaxation,” International Journal of Engineering Science, 40, pp. 587–604 (2002).Google Scholar
32.Nayfeh, A. and Nemat-Nasser, S., “Electromagneto-Thermoelastic Plane Waves in Solids with Thermal relaxation,” Journal of Applied Mechanics, E39, pp. 108–113 (1972).Google Scholar
33.Othman, M. I. A., Zidan, M. E. M. and Hilal, M. I. M., “Influence of Gravitational Field and Rotation on Thermoelastic Solid with Voids under Green-Naghdi Theory,” Journal of Physics, 2, pp. 22–34 (2013).Google Scholar
34.Kumar, R. and Rani, L., “Response of Generalized Thermoelastic Half Space with Voids due to Mechanical and Thermal Sources,” Meccanica, 39, pp. 563–584 (2004).Google Scholar
35.Mondal, A. K. and Acharya, D. P., “Surface Waves in a Micropolar Elastic Solid Containing Voids,” Acta Geophysica, 54, pp. 430–452 (2006).Google Scholar
36.Singh, J. and Tomar, S. K., “Plane Waves in Ther-mo-Elastic Material with Voids,” Mechanics of Materials, 39, pp. 932–940 (2007).Google Scholar
37.Sharma, K. and Kumar, P., “Propagation of Plane Waves and Fundamental Solution in Thermoviscoe-lastic Medium with Voids,” Journal of Thermal Stresses, 36, pp. 94–111 (2013).Google Scholar
38.Kumar, R. and Rani, L., “Mechanical and Thermal Sources in Generalized Thermoelastic Half-Space with Voids,” Journal of Pure and Applied Mathematics, 36, pp. 113–133 (2005).Google Scholar