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A generalized linear thermoelasticity theory for piezoelectric media

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Summary

A theory of thermoelasticity for piezoelectric materials which includes heat-flux among the independent constitutive variables is formulated. It is found that the linearized version of the theory admits a finite speed for thermal signals. An equation of energy balance and a theorem on the uniqueness of solution are obtained.

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References

  1. Lord, H. W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids15, 299–309 (1967).

    Google Scholar 

  2. Green, A. E., Lindsay, K. A.: Thermoelasticity. J. of Elasticity2, 1–7 (1972).

    Google Scholar 

  3. Lebon, G.: A generalized theory of thermoelasticity. J. Tech. Phys.23, 37–46 (1982).

    Google Scholar 

  4. Boschi, E., Iesan, D.: A generalized theory of linear micropolar thermoelasticity. Meccanica3, 154–157 (1972).

    Google Scholar 

  5. Dost, S., Tabbarrok, B.: Generalized micropolar thermoelasticity. Int. J. Engng. Sci.16, 173–183 (1978).

    Google Scholar 

  6. Chandrasekharaiah, D. S.: A temperature-rate dependent thermo-piezoelectricity. J. of Thermal Stresses7, 293–306 (1984).

    Google Scholar 

  7. Chandrasekharaiah, D. S.: Heat-flux dependent micropolar thermoelasticity. Int. J. Engng. Sci.24, 1389–1395 (1986).

    Google Scholar 

  8. Mindlin, R. D.: On the equations of motion of piezoelectric crystals, in: Problems of continuum mechanics, pp. 282–290 (Radok, J., ed.). Philadelphia: Society of Industrial and Applied Mathematics 1961.

    Google Scholar 

  9. Nowacki, W.: Foundations of linear piezoelectricity, in: Electromagnetic interactions in elastic solids (Parkus, H., ed.). Wien: Springer-Verlag 1979.

    Google Scholar 

  10. Maxwell, J. C.: On the dynamic theory of gases. Phil. Trans. Roy. Soc. London157, 49–88 (1867).

    Google Scholar 

  11. Peshkov, V.: Second sound in helium. II. J. Phys. USSR8, 131 (1944).

    Google Scholar 

  12. Bentman, B., Sandiford, R. J.: Second sound in solid helium. Scientific American222 (5), 92–101 (1970).

    Google Scholar 

  13. Jackson, H. E., Walker, C. T., McNelly, J. F.: Second sound in NaF. Phys. Rev. Letters25, 26–28 (1971).

    Google Scholar 

  14. Rogers, S. J.: Transport of heat and approach to second sound in some isotropically pure alkali halide crystals. Phys. Rev.3, 1440–1457 (1971).

    Google Scholar 

  15. Cattaneo, C.: On the conduction of heat. Atti del Seminario Matematics e Fisico della Universita di Modena3, 3–21 (1948).

    Google Scholar 

  16. Cattaneo, C.: A form of heat equation which eliminates the paradox of instantaneous propagation. Comptes Rendus247, 431–433 (1950).

    Google Scholar 

  17. Vernotte, P.: Paradoxes in the continuous theory of the heat equation. Comptes Rendus246, 3154–3155 (1958).

    Google Scholar 

  18. Vernotte, P.: The true heat equation. Comptes Rendus247, 2103 (1958).

    Google Scholar 

  19. Vernotte, P.: Some possible complications in the phenomenon of thermal conduction. Comptes Rendus252, 2190 (1961).

    Google Scholar 

  20. Kaliski, S.: Wave equations of heat conduction. Bull. Acad. Poln. Techn.13, 211–219 (1965).

    Google Scholar 

  21. Kaliski, S.: Wave equations of thermoelasticity. Bull. Acad. Poln. Sci. Techn.13, 253–260 (1965).

    Google Scholar 

  22. Atkin, R. J., Fox, N., Vasey, M. W.: A continuum approach to the second sound effect. J. of Elasticity5, 237–248 (1975).

    Google Scholar 

  23. Pao, Y. H., Banerjee, D. K.: A theory of anisotropic thermoelasticity at low reference temperature. J. of Thermal Stresses1, 99–112 (1978).

    Google Scholar 

  24. Toupin, R. A.: A dynamic theory of elastic dielectrics. Int. J. Engng. Sci.1, 101–126 (1963).

    Google Scholar 

  25. Tiersten, H. F.: On the non-linear equations of thermoelectroelasticity. Int. J. Engng. Sci.9, 587–604 (1971).

    Google Scholar 

  26. Hutter, K., Van de Ven, A. A. F.: Field matter interactions in thermoelastic solids (Lecture Notes in Physics, Vol. 88), Berlin: Springer-Verlag 1978.

    Google Scholar 

  27. Kaliski, S.: Wave equations of thermoelectromagnetoelasticity. Proc. Vibr. Probl.6, 231–263 (1965).

    Google Scholar 

  28. Hutter, K.: The foundations of thermodynamics, its basic postulates and implications — A review of modern thermodynamics. Acta Mech.27, 1–54 (1977).

    Google Scholar 

  29. Parkus, H.: Thermoelasticity, 2nd ed., Wien: Springer-Verlag (1976).

    Google Scholar 

  30. Chandrasekharaiah, D. S.: A uniqueness theorem in generalized thermoelasticity. J. of Techn. Phys.25, 345–350 (1984).

    Google Scholar 

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  1. Department of Mathematics, Bangalore University, Central College Campus, 560001, Bangalore, India

    D. S. Chandrasekharaiah

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  1. D. S. Chandrasekharaiah
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Chandrasekharaiah, D.S. A generalized linear thermoelasticity theory for piezoelectric media. Acta Mechanica 71, 39–49 (1988). https://doi.org/10.1007/BF01173936

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  • DOI: https://doi.org/10.1007/BF01173936

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