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Dynamical behavior of generalized thermoelastic diffusion with two relaxation times in frequency domain

  • Received : 2006.09.07
  • Accepted : 2007.09.06
  • Published : 2008.01.10

Abstract

A general solution to the field equations of homogeneous isotropic generalized thermoelastic diffusion with two relaxation times (Green and Lindsay theory) has been obtained using the Fourier transform. Assuming the disturbances to be harmonically time.dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed loads have been considered to show the utility of the solution obtained. The transformed components of displacement, stress, temperature distribution and chemical potential distribution are inverted numerically, using a numerical inversion technique. Effect of diffusion on the resulting expressions have been depicted graphically for Green and Lindsay (G-L) and coupled (C-T) theories of thermoelasticity.

Keywords

References

  1. Allam, M.N., Elasibai, K.A. and Abou Elergal, A.E. (2002), "Thermal stresses in a harmonic field for an infinite body with circular cylinder hole without energy dissipation", J. Therm. Stresses, 25, 57-67 https://doi.org/10.1080/014957302753305871
  2. Aouadi, M. (2006), "A generalized thermoelastic diffusion problem for an infinitely long solid cylinder", Int. J. Mathematics Mathematical Sci., Article ID 25976, 15
  3. Aouadi, M. (2006), "Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion", ZAMP, 57(2), 350-366 https://doi.org/10.1007/s00033-005-0034-5
  4. Boit, M. (1956), "Thermoelasticity and irreversible thermo-dynamics", J. Appl. Phys., 27, 249-253
  5. Green, A.E. and Laws, N. (1972), "On the entropy production inequality", Arch. Ration. Mech. Anal., 45, 47-53 https://doi.org/10.1007/BF00253395
  6. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7 https://doi.org/10.1007/BF00045689
  7. Kumar, R. and Rani, L. (2005), "Interaction due to mechanical and thermal sources in thermoelastic half-space with voids", J. Vib. Control, 11, 499-517 https://doi.org/10.1177/1077546305047775
  8. Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15, 299-309 https://doi.org/10.1016/0022-5096(67)90024-5
  9. Muller, I.M. (1971), "The coldness, a universal function thermoelastic bodies", Arch. Ration. Mech. Anal., 41, 319 https://doi.org/10.1007/BF00281870
  10. Nowacki, W. (1974a), "Dynamical problems of thermodiffusion in solids I", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 55-64
  11. Nowacki, W. (1974b), "Dynamical problems of thermodiffusion in solids II", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 129-135
  12. Nowacki, W. (1974c), "Dynamical problems of thermodiffusion in solids III", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 257-266
  13. Nowacki, W. (1976), "Dynamical problems of diffusion in solids", Eng. Fract. Mech., 8, 261-266 https://doi.org/10.1016/0013-7944(76)90091-6
  14. Olesiak, Z.S. and Pyryev, Y.A. (1995), "A coupled quasi-stationary problem of thermodiffusion for an elastic cylinder", Int. J. Eng. Sci., 33, 773-780 https://doi.org/10.1016/0020-7225(94)00099-6
  15. Press, W.H., Teukolshy, S.A., Vellerling W.T. and Flannery, B.P. (1986), Numerical Recipes in FORTRAN, Cambridge University Press, Cambridge
  16. Sato, R. (1969), "Formulation of solutionforearthquake source models and some related problems", J. Phys. Earth, 17, 101-110 https://doi.org/10.4294/jpe1952.17.101
  17. Schiavone, P. and Tait, R.J. (1995), "Steady time harmonic oscillations in a linear thermoelastic plate model", Quart. Appl. Math., LIII(2), 215-223
  18. Sharma, J.N., Chauhan, R.S. and Kumar, R. (2000), "Time harmonic sources in a generalized thermoelastic continuum", J. Thermal Stresses, 23, 657-674 https://doi.org/10.1080/01495730050130048
  19. Sherief, H.H. and Saleh, H. (2005), "A half-space problem in the theory of generalized thermoelastic diffusion", Int. J. Solids Struct., 42, 4484-4493 https://doi.org/10.1016/j.ijsolstr.2005.01.001
  20. Sherief, H.H., Saleh, H. and Hamza, F. (2004), "The theory of generalized thermoelastic diffusion", Int. J. Eng. Sci., 42, 591-608 https://doi.org/10.1016/j.ijengsci.2003.05.001
  21. Singh, B. (2005), "Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion", J. Earth. Syst. Sci., 114(2), 159-168 https://doi.org/10.1007/BF02702017
  22. Singh, B. (2006), "Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion", J. Sound Vib., 291(3-5), 764-778 https://doi.org/10.1016/j.jsv.2005.06.035
  23. Suhubi, E.S. (1975), Thermoelastic Solids, In: A.C. Eringen (Ed.), Continuum Physics II, Academic Press, New York, (chapter 2)

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