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On piezothermoelastic plates subject to prescribed boundary temperature

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Abstract

The thickness response of a piezothermoelastic panel, which is occupied by a material of hexagonal crystal class in a natural state, is studied under quasi-static boundary conditions with one of the bounding faces subject to prescribed temperature. It is shown that the temperature on the other bounding face can be controlled by the difference of electric potential between the faces.

Then the same matter is studied in the presence of bias fields with the electric one parallel to the polarization direction.

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References

  1. Toupin RA (1956) The elastic dielectric. J Ration Mech Anal 5:849–916

    MathSciNet  MATH  Google Scholar 

  2. Toupin RA (1963) A dynamical theory of elastic dielectrics. Int J Eng Sci 1:101–126

    Article  MathSciNet  Google Scholar 

  3. Nye JF (1957) Physical properties of crystals. Oxford University Press, New York, 356pp

    MATH  Google Scholar 

  4. Tiersten HF (1971) On the nonlinear equations of thermoelectroelasticity. Int J Eng Sci 9:587–604

    Article  MathSciNet  MATH  Google Scholar 

  5. Nowacki W (1975) Dynamic problems of thermoelasticity. Noordhoff, Gronigen, 436pp

    Google Scholar 

  6. Chandrasekharaiah DS (1988) A generalized linear thermoelasticity theory for piezoelectric media. Acta Mech 71:39–49

    Article  MATH  Google Scholar 

  7. Kalpakidis VK, Massalas CV (1993) Tiersten’s theory of thermoelectroelasticity: an extension. Int J Eng Sci 31:157–164

    Article  MathSciNet  MATH  Google Scholar 

  8. Ciarletta M, Scalia A (1994) Theory of thermoelastic dielectrics with voids. J Therm Stresses 17:529–548

    Article  MathSciNet  Google Scholar 

  9. Yang JS (2003) Equations for small fields superposed on finite biasing fields in a thermoelectroelastic body. IEEE Trans Ultrason Ferroelectr Freq Control 50(2):187–192

    Article  Google Scholar 

  10. Nowacki W (1978) Some general theorems of thermopiezoelectricity. J Therm Stresses 1:171–182

    Article  MathSciNet  Google Scholar 

  11. Montanaro A (2010) Some theorems of incremental thermoelectroelasticity. Arch Mech 62(1):49–72

    MathSciNet  Google Scholar 

  12. Ashida F, Choi JS, Noda N (1997) Control of elastic displacement in piezoelectric-based intelligent plate subjected to thermal load. Int J Eng Sci 35(9):851–868

    Article  MATH  Google Scholar 

  13. Ashida F, Tauchert TR (1997) Temperature determination for a contacting body based on an inverse piezothermoelastic problem. Int J Solids Struct 34(20):2549–2561

    Article  MATH  Google Scholar 

  14. Maira B, Münch A (2009) Exact controllability of a piezoelectric body. Theory and numerical simulation. Appl Math Optim 59:383–412

    Article  MathSciNet  Google Scholar 

  15. Yang JS (1985) Free vibrations of a pyroelectric layer of hexagonal (6 mm) class. J Acoust Soc Am 78:395–397

    Article  Google Scholar 

  16. Paul HS, Raman KGV (1991) Vibrations of pyroelectric plates. J Acoust Soc Am 90:1729–1732

    Article  ADS  Google Scholar 

  17. Eringen AC, Maugin GA (1990) Electrodynamics of continua I. Springer, New York, 436pp

    Book  Google Scholar 

  18. Yang JS (1998) Nonlinear equations of thermoviscoelectroelasticity. Math Mech Solids 3:113–124

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen WQ (2000) On the general solution for piezothermoelasticity for transverse isotropy with application. J Appl Mech 67:705–711

    Article  MATH  Google Scholar 

  20. Tiersten HF (1969) Linear piezoelectric plate vibrations. Plenum Press, New York

    Google Scholar 

  21. Eringen AC (1989) Mechanics of continua, 2nd edn. Krieger, Malabar

    Google Scholar 

  22. Sharma JN, Walia V, Gupta SK (2008) Effect of rotation and thermal relaxation on Rayleigh waves in piezothermoelastic half space. Int J Mech Sci 50:433–444

    Article  Google Scholar 

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Montanaro, A. On piezothermoelastic plates subject to prescribed boundary temperature. Meccanica 46, 383–398 (2011). https://doi.org/10.1007/s11012-010-9320-1

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  • DOI: https://doi.org/10.1007/s11012-010-9320-1

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