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Axi-Symmetric Deformation in Generalized Thermoelasticity with Two Temperatures

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Abstract

The disturbance due to normal force and thermal source in a homogeneous, isotropic generalized thermoelastic medium with two temperatures for the axi-symmetric problem in the context of generalized theories [Lord and Shulman (L-S) theory and Green–Lindsay (G-L) theory] are obtained by applying the Laplace and Hankel transforms. To get the solution in physical form, a numerical inversion technique has been applied. The components of stress, conductive temperature \({\phi}\) and temperature distribution θ are computed numerically and illustrated graphically to compare the results between the two temperature models for L-S and G-L as well as for classical one temperature theory of thermoelasticity. Some special cases are also deduced from the present problem.

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References

  1. Boley M.: Thermoelastic and irreversible thermo dynamics. J. Appl. Phys. 27, 240–253 (1956)

    Article  MathSciNet  Google Scholar 

  2. Chen P.J., Gurtin M.E.: On a theory of heat conduction involving two temperatures. ZAMP 19, 614–627 (1968)

    Article  MATH  Google Scholar 

  3. Chen P.J., Gurtin M.E., Willams W.O.: On the thermodynamics of non-simple Elastic material with two temperature. Z. Angew Math. Phys. 20, 107–112 (1969)

    Article  MATH  Google Scholar 

  4. Dhaliwal, R.S.; Singh, A.: Dynamic coupled thermoelasticity, p. 726. Hindustan Publisher Corp, New Delhi (1980)

  5. Green A.E., Lindsay K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)

    Article  MATH  Google Scholar 

  6. Kumar R., Pratap G.: Axi-symmetric free vibration of infinite micropolar thermoelastic plate. AMM 28, 364–383 (2007)

    Google Scholar 

  7. Kumar R., Singh R., Chadha T.K.: Axi-symmetric problem in microstretch elastic solid. Indian J. Math. 44, 147–164 (2002)

    MathSciNet  MATH  Google Scholar 

  8. Lord H.W., Shulman Y.: A Generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)

    Article  MATH  Google Scholar 

  9. Press W.H., Teukolshy S.A., Vellerling W.T. et al.: Numerical Recipes in FORTRAN, 2nd edn. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  10. Quintanilla R.: On existence, structural stability, convergence and spatial behaviour in thermoelastic with two temperature. Acta Mech. 168, 161–173 (2004)

    Article  Google Scholar 

  11. Quintanilla R.: Exponential stability and uniqueness in thermoelasticity with two temperature. Ser. A Math. Anal. 11, 57–68 (2004)

    MathSciNet  MATH  Google Scholar 

  12. Sherief H.H., Saleh H.: A half-space problem in the theory of generalized thermoelastic diffusion. Int. J. Solids Struct. 42, 4484–4493 (2005)

    Article  MATH  Google Scholar 

  13. Warren W.E., Chen P.J.: Wave propagation in the two temperature theory of thermoelasticity. Acta Mech. 16, 21–23 (1973)

    Article  MATH  Google Scholar 

  14. Youssef, H.M.: Theory of two temperature generalized thermoelastic. IMA J. Appl. Math. 1–8 (2005)

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Authors and Affiliations

  1. Department of Mathematics, C.D.L. University, Sirsa, India

    Aseem Miglani

  2. Department of Mathematics, M.M.E.C. Maharishi Markandeshwar University, Mullana (Ambala), India

    Sachin Kaushal

Authors
  1. Aseem Miglani
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  2. Sachin Kaushal
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Correspondence to Sachin Kaushal.

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Miglani, A., Kaushal, S. Axi-Symmetric Deformation in Generalized Thermoelasticity with Two Temperatures. Arab J Sci Eng 36, 1581–1595 (2011). https://doi.org/10.1007/s13369-011-0139-4

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  • DOI: https://doi.org/10.1007/s13369-011-0139-4

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