Mathematical model of generalized thermoelastic infinite medium with a spherical cavity and fractional order strain

Volume 12, Issue 1, pp 30--37 http://dx.doi.org/10.22436/jnsa.012.01.03

Publication Date: September 30, 2018 Submission Date: June 11, 2018 Revision Date: August 05, 2018 Accteptance Date: August 31, 2018

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Authors

Eman A. N. Al-Lehaibi - Mathematics Department, College of Science and Arts-Sharoura, Najran University, KSA.

Abstract

In this paper, a new mathematical model of a thermoelastic isotropic unbounded medium contains a spherical cavity thermally shocked under generalized thermo-elasticity with the fractional order strain model. The governing system of the partial differential equations has been derived in Laplace transform domain, and the inversion was done numerically by using the sum of Riemann approximation techniques. The numerical outputs of the displacement, the temperature, the stress, and the strain have been obtained and presented graphically. The fractional order parameter has an essential consequence on the stress, the strain, and the displacement distributions while its effect on the temperature increment distribution is very limited.

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Keywords

• Generalized thermo-elasticity
• spherical cavity
• fractional calculus
• fractional strain

MSC

•  74B20
•  74F05
•  35R11
•  65R10

References

• [1] N. S. Al-Huniti, M. Al-Nimr, M. Naji , Dynamic response of a rod due to a moving heat source under the hyperbolic heat conduction model , J. Sound Vib., 242 (2001), 629–640.
  • View Article
  • Google Scholar


• [2] M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27 (1956), 240–253.
  • View Article
  • MathSciNet
  • Google Scholar


• [3] S. Erbay, E. S. Suhubi , Longitudinal wave propagation in a generalized thermoelastic cylinder, J. Therm. Stresses, 9 (1986), 279–295.
  • View Article
  • Google Scholar


• [4] T. Furukawa, N. Noda, F. Ashida , Generalized thermoelasticity for an infinite body with a circular cylindrical hole, JSME Int. J. I-Solid M., 33 (1990), 26–32.
  • View Article
  • Google Scholar


• [5] A. E. Green, N. Laws, On the entropy production inequality, Arch. Rational Mech. Anal., 45 (1972), 47–53.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] A. E. Green, K. A. Lindsay , Thermoelasticity, J. Elasticity, 2 (1972), 1–7.
  • View Article
  • Google Scholar


• [7] H. W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15 (1967), 299–309.
  • View Article
  • Google Scholar


• [8] R. L. Magin, T. J. Royston , Fractional-order elastic models of cartilage: A multi-scale approach, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 657–664.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] J. C. Misra, N. C. Chattopadhyay, S. C. Samanta , Thermoviscoelastic waves in an infinite aeolotropic body with a cylindrical cavity–a study under the review of generalised theory of thermoelasticity, Computers & structures, 52 (1994), 705–717.
  • View Article
  • Google Scholar
  • MATH


• [10] J. C. Misra, S. C. Samanta, A. K. Chakrabarti, S. C. Misra, Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating, Int. J. Eng. Sci., 29 (1991), 1505–1514.
  • View Article
  • Google Scholar
  • MATH


• [11] I. Mller , The Coldness, a Universal Function in Thermo-Elastic Solids, Arch. Rat. Mech. Anal., 41 (1971), 319–332.
  • Google Scholar


• [12] J. L. Schiff , The Laplace transform: theory and applications, Springer Science & Business Media, New York (2013)
  • Google Scholar


• [13] H. H. Sherief, M. N. Anwar, Two-dimensional generalized thermoelasticity problem for an infinitely long cylinder, J. Thermal Stresses, 17 (1994), 213–227.
  • View Article
  • Google Scholar


• [14] E. S. Suhubi , Thermoelastic solids: Continuum Mechanics of Single-Substance Bodies, Elsevier, 1975 (1975), 173–265.
  • Google Scholar


• [15] D. Y. Tzou, Macro-to microscale heat transfer: the lagging behavior, John Wiley & Sons, U.S.A. (2014)
  • Google Scholar


• [16] H. M. Youssef , Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity , Appl. Math. Mech., 26 (2005), 470–475.
  • View Article
  • Google Scholar
  • MATH


• [17] H. M. Youssef , State-space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp-type heating , Can. Appl. Math. Q., 13 (2005), 369–390.
  • MathSciNet
  • Google Scholar
  • MATH


• [18] H. M. Youssef , Theory of generalized thermoelasticity with fractional order strain , J. Vib. Control, 22 (2016), 3840–3857.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH