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Tytuł artykułu

Uniqueness, reciprocity theorems and plane wave propagation in different theories of thermoelasticy

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Języki publikacji
EN
Abstrakty
EN
In this work, a compact form of different theories of thermoelasticity is considered. The governing equations for particle motion in a homogeneous isotropic thermoelastic medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in a homogeneous isotropic thermoelastic medium is studied. For a three dimensional problem there exist four waves, namely a P-wave, two transverse waves (S1, S2) and a thermal wave (T). From the obtained results the different characteristics of waves such as the phase velocity and attenuation coefficient are computed numerically and presented graphically. Some special cases are also discussed.
Rocznik
Strony
1067--1086
Opis fizyczny
Bibliogr. 29 poz., wykr.
Twórcy
autor
  • Department of Mathematics, Kurukshetra University Kurukshetra 136119, Haryana INDIA
autor
  • Department of Mathematics, Kurukshetra University Kurukshetra 136119, Haryana INDIA
Bibliografia
  • Aouadi M. (2007): Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion. - J. Thermal Stresses, vol.30, pp.665-678.
  • Aouadi M. (2008): Generalized theory of thermoelastic diffusion for anisotropic media. - J. Thermal Stresses, vol.31, pp.270-285.
  • Banergee D.K. and Pao Y.H. (1974): Thermoelastic waves in anisotropic solids. - J. Acoust. Soc. Am., vol.56, pp.1444-1456.
  • Biot M.A. (1956): Thermoelasticity and irreversible thermodynamics. - J. Appl. Phys., vol.27, p.40.
  • Catteneo C. (1958): Sur une forme de l’equation de la Chaleur eliminant le paradoxe d’une propagation instantane’e. - C. R. Acad. Sci., vol.247, pp.431-433.
  • Chadwick P. (1979): Basic properties of plane harmonic waves in a prestressed heat conducting elastic materials. - J.Therm. Stress., vol.2, pp.193-214.
  • Chadwick P. and Sheet L.T.C. (1970): Wave propagation in transversely isotropic heat conducting elastic materials. - Mathematika, vol.17, pp.255-272.
  • Chandrasekharaiah D.S. (1998): Hyperbolic thermoelasticity: A review of recent literature. - Appl. Mech. Rev., vol.51, pp.705-729.
  • Churchill R.V. (1972): Operational Mathematics. 3rd edition. - New York: McGraw-Hill.
  • Dhaliwal R.S. and Sherief H.H. (1981): A reciprocity theorem and integral representations for generalized thermoelasticity. - J. Math. Phys. Sci., vol.15, pp.537-549.
  • El-Karmany A.S. and Ezzat M.A. (2011): Convolutional variational principle, rciprocal and uniqueness theorems in linear fractional two-temperature thermoelasticity. - J. Thermal Stresses, vol.34, pp.264-284.
  • Ezzat M.A. and El-Karmany A.S. (2002): The uniqueness and reciprocity theorems for generalized thermoviscoelasticity with two relaxation times. - Int. J. Eng. Sci., vol.40, pp.1274-1284.
  • Green A.E. and Lindsay K.A. (1972): Thermoelasticity. - J. Elasticity, vol.2, pp.1-7.
  • Green A.E. and Nagdhi P.M. (1991): A reexamination of the basic posulates of thermomechanics. - Proc. Royal Soc.Lond., vol.432, pp.171-194.
  • Green A.E. and Nagdhi P.M. (1992): Thermoelasticity without energy dissipation. - J. Elasticity, vol.31, pp.189-208.
  • Hetnarski R.B. and Ignaczak J. (1996): Solution-like waves in a low temperature non-linear thermoelastic solid. - Int. J.Eng. Sci., vol.34, pp.1767-1787.
  • Hetnarski R.B. and Ignaczak J. (1999): Generalized thermoelasticity. - J. Therm. Stress., vol.22, pp.451- 476.
  • Iesan D. (1986): A theory of thermoelastic materials with voids. - Acta Mechanica, vol.60, pp.67-89.
  • Ignaczak J. (1982): A note on uniqueness in thermoelasticity with one relaxation time. - J. Therm. Stress., vol.5, pp.257-263.
  • Kumar R. and Kansal T. (2010): Analysis of plane waves in anisotropic thermoelastic diffusive medium. - Mechanics of Solids, vol.47, pp.337-356.
  • Lord H.W. and Shulman Y. (1967): Generalized dynamical theory of thermoelasticity. - J. Mech. Phys. Solid, vol.15, pp.299-309.
  • Roychoudhary S.K. (2007): On a thermoelastic three-phase-lag model. - J. Therm. Stress., vol.30, pp.231-238.
  • Sharma M.D. (2010): Existance of longitudinal and transverse waves in anisotropic thermoelastic media. - Acta Mech., vol.209, pp.275-283.
  • Sherief H.H. (1987): On uniqueness and stability in generalized thermoelasticity. - Quart. Appl. Math., vol.45, pp.773-778.
  • Sherief H.H. and Dhaliwal R.S. (1980): A uniqueness theorem and a variational principle for generalized thermoelasticity. - J. Therm. Stress., vol.3, pp.223-230.
  • Sherief H.H. and Saleh H.A. (?) A half space problem in the theory of thermoelastic diffusion. - International Journal of Solid and Structures, vol.42, pp.4484-4493.
  • Sherief H.H., El-Said A. and Abd El Latief A. (2010): Fractional order theory of thermoelasticity. - Int. J. Solid Struct. vol.47, pp.269-275.
  • Sherief H.H., Saleh H. and Hamza F. (2004): The theory of generalized thermoelastic diffusion. - Int. J. Engg. Sci., vol.42, pp.591-608.
  • Tzou D.Y. (1995): A unified field approach for heat conduction from macro to microscales. - ASME J. Heat Transf., vol.117, pp.8-16.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2f084023-d412-40d0-8ec6-3439e1c0e0e2
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