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The Thermal Relaxation Effect on 2-D Problems of the Generalized Linear Thermo-Viscoelasticity

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Języki publikacji
EN
Abstrakty
EN
In this paper we introduced the normal mode analysis for two-dimensional problems of the generalized linear thermo-viscoelasticity with one relaxation time. The exact expressions for the temperature distribution, the displacement components and the stress are obtained. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face. The second concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-viscoelastic half-space subjected to appropriate boundary conditions and the third problem deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory.
Rocznik
Strony
45--62
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
  • Faculty of Education, Department of Mathematics, Salalah-211, P.O. Box 2801, Sultanate of Oman, m_i_othman@yahoo. com
Bibliografia
  • [1] Gross, B.: Mathematical structure of the theories of viscoelasticity, Hemann, Paris, (1953).
  • [2] Staverman, A.J. and Schwarzl, F.: Die physik der hochpolymeren, Ed. H.A. Stuart, vol. 4, Springer Verlag, Ch.l, (1956).
  • [3] Alfrey, T. and Gurnee, E.F.: Rheology theory and applications, Ed. F.R. Eirich, vol. 1, Academic Press, New York, (1956).
  • [4] Ferry, J.D.: Viscoelastic properties of polymers, J. Wiley and Sons, New York, (1970).
  • [5] Biot, M.A.: Theory of stress-strain relations in an isotropic viscoelasticity, and Relaxation phenomena, J. Applied Physics, 25, (1954).
  • [6] Biot, M.A.: Variational principal in irreversible thermodynamics with application to viscoelasticity, Physical Review, 97, (1955).
  • [7] Huilgol, R. and Phan-Thien, N.: Fluid mechanics of viscoelasticity, Elsevier, (1997).
  • [8] Bland, D.R.: The theory of linear viscoelasticity, Oxford, Pergamon Press, (1960).
  • [9] Gurtin, M.E. and Sternberg, E.: On the linear theory of viscoelasticity, Arch. Ration. Mech. Anal., 11, (1962).
  • [10] Ilioushin, A.A.: The approximation method of calculating the constructures by linear thermal viscoelastic theory, Mekhanika Polimerov, Riga 2, (1968).
  • [11] Ilioushin, A.A. and Pobedria, B.E.: Mathematical theory of thermal viscoelasticity, Nauka, Moscow, (1970).
  • [12] Pobedria, B.E.: Coupled problems in continuum mechanics. J. Durability and plasticity, No. l, Moscow State University, Moscow, (1984).
  • [13] Koltunov, M.A.: Creeping and relaxation, Moscow, (1976).
  • [14] Biot, M.: Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 240, (1956).
  • [15] Lord, H. and Shulman. Y.: A generalized dynamical theory of thermo-elasticity, J. Mech. Phys. Solid, 15, 299, (1967).
  • [16] Dhaliwal, R. and Sherief, H. H.: Generalized thermoelasticity for an isotropic media, Quart. Appl. Math., 33, 1, (1980).
  • [17] Othman, M.I.A, Ezzat, M.A., Zaki, S.A, and El-Karamany, A. S.: Generalized thermoviscoelastic plane waves with two relaxation times, Int. J. Engng. Sci., 40, 1329-1347, (2002).
  • [18] Othman, M.I. A.: The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with different relaxation times, Mechanics and Mechanical Engineering, 7, No.2, 77-88, (2004).
  • [19] Othman, M.I.A.: Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time, Ada Mechanica, 169, 37-51, (2004).
  • [20] Othman, M.I. A.: Effect of rotation and relaxation time on a thermal shock problem for a half-space in generalized thermo-viscoelasticity, Acta Mechanica, accepted in 8/9/2004, to appear.
  • [21] Fung, Y.C.: Foundation of solid mechanics, Prentice-Hall, N.D., (1968).
  • [22] Sherief, H.H. and Anwar, M.A.: Generalized thermo-elasticity for a plane subjected to moving heated sources on both sides, J. Thermal Stresses, 15, 489, (1992).
  • [23] Sherief, H.H. and Anwar, M.A.: Two-dimensional problem of moving heated punch in generalized thermo-elasticity, J. Thermal Stresses, 9, 325, (1986).
  • [24] Othman, M.I.A.: Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermo-elasticity, J. Thermal Stresses, 25, 1027-1045, (2002).
  • [25] Othman, M.I.A.: Electrohydrodynamic instability of a rotating layer of a visco-elastic fluid heated from below, ZAMP, 55, 468-482, (2004).
  • [26] Othman, M.I.A.: Electrohydrodynamic stability in a horizontal viscoelastic fluid layer in the presence of a vertical temperature gradient, Int. J. Engng. Sci., 39, 1217- 1232, (2001).
  • [27] Othman, M.I.A. and Zaki, S.A.: Thermal relaxation effect on magneto-hydro-dynamic instability in a rotating micropolar fluid layer heat generation, Acta Mechanica, 70, 178-197, (2004).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0019-0013
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