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The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation times

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The equations of generalized thermo-viscoelasticity based on Lord-Shulman (L-S), Green and Lindsay (G-L) and Classical dynamical coupled (CD) theories are given. Using Laplace transforms, a uniqueness theorem for these equations is proved. Also, a reciprocity theorem is obtained.
Rocznik
Strony
77--87
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Faculty of Education, Department of Mathematics, Salalah-211, P.O. Box 2801, Sultanate of Oman, m_i_othman@yahoo.com
Bibliografia
  • [1] Biot, M: Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., (1956), 27, 240.
  • [2] Lord, H, Shulman, Y: A Generalized dynamic cal theory of thermo-elasticity, J. Mech. Phys. Solid, (1976), 15, 299-309.
  • [3] Dhaliwal, R, Sherief, H: Generalized thermoelasticity for an isotropic media, Quart. Appl. Math., (1980), 33, 1-8.
  • [4] Ezzat, MA, Othman, MIA, El Karamany, AS: State space approach to two-dimensional generalized thermo-viscoelasticity with one relaxation time, J. of Thermal Stresses, (2002), 25, 295-316.
  • [5] Müller, I: The Coldness, A Universal function in thermo-elastic Solids, Arch. Rat. Mech. Anal., (1971), 41, 319.
  • [6] Green, AE, Laws, N: On the entropy production inequality, Arch. Rat. Mech. Anal., (1972), 45, 47.
  • [7] Green, AE, Lindsay, KA: Thermoelasticity, Journal of Elasticity, (1972), 2, 1.
  • [8] Suhubi, ES: Thermoelastic solids, in: Continuum Physics II, Ch. 2, Eringen, AC, Ed., (1975), Academic, Press, New York.
  • [9] Ignaczak, J: A strong discontinuity wave in thermoelastic with relaxation times, J. Thermal Stresses, (1985), 8, 25-40.
  • [10] Ignaczak, J: Decomposition theorem for thermoelasticity with finite wave speeds, J. Thermal Stresses, (1985), 1, 41.
  • [11] Ezzat, MA, Othman, MIA, El Karamany, AS: State space approach to generalized thermo-viscoelasticity with two relaxation times, (2002), Int. J. Engng. Sci., 40, 283-302.
  • [12] Ezzat, MA, Othman, MIA, El Karamany, AS: State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times, J. Engng. Sci., (2002), 40, 1251-1274.
  • [13] Ezzat, MA, Othman, MIA: State space approach to generalized magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity, J. Thermal Stresses, (2002), 25, 409-429.
  • [14] Gross, B: Mathematical structure of the theories of viscoelasticity, (1953), Hermann, Paris.
  • [15] Staverman, AJ, Schwarzl, F: Die Physik der hochpolymeren, Stuart, HA, Ed., (1956), 4, Springer Verlag, Chapter 1.
  • [16] Alfrey, T, Gurnee, EF: Rheology theory and applications, Eirich, FR, Ed., l, (1956), Academic Press, New York.
  • [17] Ferry, JD: Viscoelastic properties of polymers, (1970), John Wiley & Sons, New York.
  • [18] Fung, YC: Foundation of solid mechanics, (1980), Prentice-Hall, Englewood Cliffs, NJ.
  • [19] Pobedria, BE: Coupled problems in continuum mechanics, J. Durabilility and Plasticity, Moscow State University, Moscow.
  • [20] Sternberg, E: On the analysis of thermal stresses in viscoelastic solids, Brown Univ. Dir, J. Appl. Math. TR., (1963), 9, 213-219.
  • [21] Ilioushin, AA, Pobederia, BE: Mathematical theory of thermal viscoelastic, (1970), Nauka, Moscow.
  • [22] Boley, B, Weiner, JH: Theory of thermal stresses, (1960), John Wiley & Sons, Inc. New York.
  • [23] Churchill, RV: Operational mathematics, third ed., (1972), McGraw-Hill, New York.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0022-0055
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