Advertisement

Moving Heat Source Response in a Thermoelastic Microelongated Solid

  • S. Shaw
  • B. Mukhopadhyay
Article

The present paper deals with thermoelastic interactions in a microelongated, isotropic, homogeneous medium in the presence of a moving heat source. In this context, the generalized theory of heat conduction is considered. In order to illustrate the results obtained, a numerical solution for aluminum epoxy-like material is obtained, and the variations of the displacement, microelongation, normal strain, and normal stress are presented. The results may be applied for damage characterization of materials.

Keywords

moving heat source microelongation microstretch generalized heat conduction equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 240–253 (1956).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    S. Kaliski, Wave equation of heat conduction, Bull. Acad. Pol. Sci., Ser. Sci. Tech., 13, 211–219 (1965).Google Scholar
  3. 3.
    S. Kaliski, Wave equation of thermoelasticity, Bull. Acad. Pol. Sci., Ser. Sci. Tech., 13, 253–360 (1965).Google Scholar
  4. 4.
    H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299–309 (1967).MATHCrossRefGoogle Scholar
  5. 5.
    A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast., 2, 1–7 (1972).MATHCrossRefGoogle Scholar
  6. 6.
    A. C. Eringen and E. S. Suhubi, Nonlinear theory of simple microelastic solids, Int. J. Eng. Sci., 2, 189–203, 389–404 (1964).MathSciNetGoogle Scholar
  7. 7.
    A. C. Eringen, Microcontinuum Field Theories, Vol. 1, Foundations and Solids, Springer Verlag, New York (1999).CrossRefGoogle Scholar
  8. 8.
    A. C. Eringen, Micropolar elastic solids with stretch, Ari Kitabevi Matbassi, 24, 1–18 (1971)Google Scholar
  9. 9.
    A. C. Eringen, Theory of thermomicrostretch elastic solids, Int. J. Eng. Sci., 28, 1291–1301 (1990).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    A. C. Eringen, Linear theory of micropolar elasticity, J. Math. Mech., 15, 909–923 (1966).MathSciNetMATHGoogle Scholar
  11. 11.
    A. C. Eringen, Theory of micropolar fluids, J. Math. Mech., 15, 1–18 (1966).Google Scholar
  12. 12.
    A. Kiris and E. Inan, Eshelby tensors for a spherical inclusion in microelongated elastic fields, Int. J. Eng. Sci., 43, 49–58 (2005).MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    B. Singh and R. Kumar, Wave propagation in a generalized thermomicrostretch elastic solid, Int. J. Eng. Sci., 36, 891–912 (1998).MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    J. N. Sharma, S. Kumar, and Y. D. Sharma, Effect of micropolarity, microstretch and relaxation times on Rayleigh surface waves in thermoelastic solids, Int. J. Appl. Math. Mech., 5, No. 2, 17–38 (2009).Google Scholar
  15. 15.
    R. Quintanilla, On spatial decay for the dynamic problem of thermomicrostretch elastic solid, Int. J. Eng. Sci., 40, 299–309 (2002).Google Scholar
  16. 16.
    A. C. Eringen, Electromagnetic theory of microstretch elasticity and bone modeling, Int. J. Eng. Sci., 42, 231–242 (2004).MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    H. M. Youssef, State-space in generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp-type heating, Can. Appl. Math. Qu., 13, No. 4, 369–390 (2005).MathSciNetMATHGoogle Scholar
  18. 18.
    H. M. Youssef, The dependence of the modulus of elasticity and thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26, No. 4 (2005).Google Scholar
  19. 19.
    H. M. Youssef, Generalized thermoelastic infinite medium with spherical cavity subjected to moving heat source, Comp. Math. Mode., 21, No. 2, 211–225 (2010).Google Scholar
  20. 20.
    A. Kiris and E. Inan, 3-D vibration analysis of the rectangular microdamaged plates, in: Proc. 8th Int. Conf. on Vibration Problems (ICOVP), India (2007), pp. 207–214.Google Scholar
  21. 21.
    S. De Cicco and L. Nappa, On the theory of thermomicrostretch elastic solids, J. Thermal Stresses, 22, 565–580 (1999).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsBengal Engineering and Science UniversityPin-India

Personalised recommendations