Rheological Consequence of the Behavior of Thermoviscoelastic Substances in the Presence of an Instantaneous Point Heat Source

1. H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299–309 (1967).

   Article  MATH  Google Scholar 

2. A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elasticity, 2, 1–7 (1972).

   Article  MATH  Google Scholar 

3. A. D. Drozdov, A constitutive model in thermoviscoelasticity, Mech. Res. Commun., 23, 543–548 (1996).

   Article  MATH  Google Scholar 

4. M. I. A. Othman and Y. Song, Effect of rotation on plane waves of generalized electromagneto-thermo-viscoelasticity with two relaxation times, Appl. Math. Model., 32, 811–825 (2008).

   Article  MathSciNet  MATH  Google Scholar 

5. A. Kar and M. Kanoria, Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect, Appl. Math. Model., 33, 3287–3298 (2009).

   Article  MathSciNet  MATH  Google Scholar 

6. M. A. Ezzat, M. Zakaria, and A. S. El-Karamany, Effects of modifi ed Ohm’s and Fourier’s laws on generalized magnetoviscoelastic thermoelasticity with relaxation volume properties, Int. J. Eng. Sci., 48, 460–472 (2010).

   Article  MathSciNet  MATH  Google Scholar 

7. M. R. Kundu and B. Mukhopadhyay, A thermoviscoelastic problem of an infi nite medium with a spherical cavity using generalized theory of thermoelasticity, Math. Comput. Model., 41, 25–32 (2005).

   Article  MATH  Google Scholar 

8. M. K. Mondal and B. Mukhopadhyay, A two-temperature thermo-visco-elastic problem with rheological properties, Int. J. Appl. Math. Mech., 9, 51–68 (2013).

   Google Scholar 

9. J. D. Ferry, Mechanical properties of substances of high molecular weight. Dispersion in concentrated polymer solutions and its dependence on temperature and concentration, J. Am. Chem. Soc., 72, 37–46 (1953).

10. M. Aouadi and A. S. El-Karamany, The relaxation effects of volume properties in two-dimensional generalized thermoviscoelastic problem, Appl. Math. Comput., 151, 689–711 (2004).

    Article  MathSciNet  MATH  Google Scholar 

11. R. Muki and E. Sternberg, On transient thermal stresses in visco-elastic material with temperature dependent properties, J. Appl. Mech., 28, 193–207 (1961).

    Article  MathSciNet  MATH  Google Scholar 

12. M. Aouadi, Generalized thermo-piezoelectric problem with temperature-dependent properties, Solids Struct., 43, 6347–6358 (2006).

    Article  MATH  Google Scholar 

13. M. K. Mondal and B. Mukhopadhyay, A cylindrical problem with rheological volume, density property on thermovisco-elastic medium in magnetic fi eld, Int. J. Appl. Math. Mech., 9, No. 2, 22–38 (2013).

    Google Scholar 

14. A. S. El-Karamany, Deformation of a non-homogeneous viscoelastic hollow space, Eng. Trans., Warsaw, 31, 267 (1983).

15. V. A. Lomakin, The Theory of Elasticity of Non-Homogeneous Bodies, Moscow State University Press, Moscow (1976).

    Google Scholar 

16. R. Bellman, R. E. Kalaba, and J. A. Lockett, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York (1966).

    MATH  Google Scholar 

17. M. A. Ezzat, M. I. Othman, and A. S. El-Karamany, State space approach to generalized thermoviscoelasticity with two relaxation times, Int. J. Eng. Sci., 40, 283–302 (2002).

    Article  MATH  Google Scholar 

18. W. Nowacki, Some dynamic problems of thermoviscoelasticity, Arch. Mech. Stos., 11, 259–283 (1959).

    MathSciNet  MATH  Google Scholar 

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