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Variational principles for generalized dynamical theory of thermopiezoelectricity

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Abstract

The universal thermodynamic variational principle proposed in the previous papers for nonlinear dielectrics is extended to the thermopiezoelectricity and it is used as a fundamental physical principle to derive the simple complete governing equations of the generalized dynamical theory of thermopiezoelectricity in this paper. In the generalized dynamical theory it is assumed that the acceleration of the temperature needs the extra increment of the heat and the inertial entropy is proposed.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Shen S.P., Kuang Z.-B.: An active control model of laminated piezothermoelastic plate. Int. J. Solids Struct. 36, 1925–1947 (1999)

    Article  MATH  Google Scholar 

  3. Chen C., Shen Y., Tian X.: Variational principles of nonlinear piezothermoelastic media. Acta Mech. Solida Sin. 11, 13–27 (1998)

    Google Scholar 

  4. Lord H.W., Shulman Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)

    Article  MATH  Google Scholar 

  5. Green, A.E., Lindsay: Thermoelasticity. J. Elast. 2, 1–7 (1972)

  6. Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chandrasekharaiah D.S.: A temperature-rate-dependent theory of thermopiezoelasticity. J. Therm. Stress 7, 293–306 (1984)

    Article  MathSciNet  Google Scholar 

  8. Kuang Z.-B.: Some problems in electrostrictive and magnetostrictive materials. Acta Mech. Solida Sin. 20, 219–227 (2007)

    Google Scholar 

  9. Kuang Z.-B.: Some variational principles in elastic dielectric and elastic magnetic materials. Eur. J. Mech. A/Solids 27, 504–514 (2007)

    Article  MathSciNet  Google Scholar 

  10. De Groet S.R.: Thermodynamics of Irreversible Processes. North-Holland Publishing Company, Amsterdam (1952)

    Google Scholar 

  11. Germain P., Nguyen Q.S., Suquet P.: Continuum thermodynamics. J. Appl. Mech. 50, 1010–1020 (1983)

    Article  MATH  Google Scholar 

  12. Kuang, Z.-B.: Nonlinear Continuum Mechanics. Shanghai Jiaotong University Press, Shanghai (2002, in Chinese)

  13. Kuang, Z.B.: General variational principle and the theory of the plate. In: Scientific report of Xi’an Jiaotong University, Xi’an (1964, in Chinese)

  14. Singh B.: On the theory of generalized thermoelasticity for piezoelectric materials. Appl. Math. Comput. 171, 398–405 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China

    Zhen-Bang Kuang

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  1. Zhen-Bang Kuang
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Correspondence to Zhen-Bang Kuang.

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Kuang, ZB. Variational principles for generalized dynamical theory of thermopiezoelectricity. Acta Mech 203, 1–11 (2009). https://doi.org/10.1007/s00707-008-0039-1

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  • DOI: https://doi.org/10.1007/s00707-008-0039-1

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