Skip to main content
SpringerLink
Log in

Plane waves in pyroelectrics with viscous effect

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The present paper analyzes the propagation of plane waves in an infinite pyroelectric medium. In order to consider the real situation, a new thermo-electric-elastic model with viscous effect is presented. The theoretical analysis shows that the elastic viscous effect and the Fourier’s law are in the same level in the evolution equations. So, the thermal viscous effect in Cattaneo’s equation belongs to a second-order effect. Numerical calculations are performed for pyroelectric material BaTiO3 using three models (Kaliski–Lord–Shulman theory, inertial entropy theory and inertial entropy with viscous effect). Results show that the elastic viscous relaxation time τ 0 plays a large role on the mechanical waves and admits mechanical waves decaying in propagation process. The effects of the thermo-relaxation time τ s on the attenuation of mechanical waves are also researched and discussed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hadni A.: Applications of the pyroelectric effect. J. Phys. E-Sci. Instrum. 14(11), 1233–1240 (1981)

    Article  Google Scholar 

  2. Biot M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 249–253 (1956)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Tiersten H.E.: On the nonlinear equations of thermo-electroelasticity. Int. J. Eng. Sci. 9, 587–604 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  5. Mindlin R.D.: Equations of high frequency vibrations of thermopiezoelectric crystal plates. Int. J. Solids Struct. 10, 625–637 (1974)

    Article  MATH  Google Scholar 

  6. 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 

  7. Landau L.: The theory of superfluidity of helium II. J. Phys. 5, 71 (1941)

    Google Scholar 

  8. Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford University Press, New York (2010)

  9. Yuan X.G., Kuang Z.B.: Waves in pyroelectrics. J. Therm. Stress. 31(12), 1190–1211 (2008)

    Article  Google Scholar 

  10. Yuan X.G., Kuang Z.B.: The inhomogeneous waves in pyroelectrics. J. Therm. Stress. 33, 172–186 (2010)

    Article  Google Scholar 

  11. Kuang Z.B.: Two theoretical problems in electro-magneto-elastic analysis. Acta Mecha. 224, 1201–1212 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mineev V.N., Mineev A.V.: Viscosity of metals under shock-loading conditions. J. De Phys. IV 7(C3), 583–585 (1997)

    Google Scholar 

  13. Zhang W.J., Liu C.L.: Effective viscosity coefficients, initial mobile dislocation densities and drag stresses for five materials. Chin. J. High Press. Phys. 20(4), 345–352 (2006) (in Chinese)

    Google Scholar 

  14. Ma X.J., Liu F.S., Zhang M.J., Sun Y.Y.: Viscosity of aluminum under shock-loading conditions. Chin. Phys. B 20(6), 068301–068304 (2011)

    Article  Google Scholar 

  15. Lionetto F., Montagna F., Maffezzoli A.: Ultrasonic dynamic mechanical analysis of polymers. Appl. Rheol. 15, 326–335 (2005)

    Google Scholar 

  16. Xu H.Y., Zhang Y.C., Song Y.Q., Chen D.Y.: Thermal shock problem for a semi-infinite thermo-viscoelastic piezoelectric rod with thermal relaxation. Micro. Tech. 8, 30–37 (2004) (in Chinese)

    Google Scholar 

  17. Kaliski S.: Wave equation of thermoelasticity. Bulletin de l’Academie Polonaise des Sciences. Serie des Sci. Tech. 13, 211–219 (1965)

    Google Scholar 

  18. Lord H.W., Shulman Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Kuang Z.B.: Variational principles for generalized dynamical theory of thermo-piezoelectricity. Acta Mech. 203, 1–11 (2009)

    Article  MATH  Google Scholar 

  21. Cattaneo C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus 247, 431–433 (1958)

    MathSciNet  Google Scholar 

  22. Joseph D.D., Preziosi L.: Heat waves. Rev. Morden Phys. 61, 41–73 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  23. Eringen A.C.: Nonlinear Theory of Continuous Media. McGraw-Hill, New York (1962)

    Google Scholar 

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

  25. Sharma J.N., Walia V.: Further investigations on Rayleigh waves in piezothermoelastic materials. J. Sound Vib. 301, 189–206 (2007)

    Article  Google Scholar 

  26. Sharma J.N., Walia V., Gupta S.K.: Reflection of piezothermoelastic waves from the charge and stress boundary of a transversely isotropic half space. Int. J. Eng. Sci. 46, 131–146 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  27. Brock L.M.: Plane waves with dispersion and decay: surface reflection for thermoelastic solids with thermal relaxation. J. Therm. Stress. 34, 687–701 (2011)

    Article  Google Scholar 

  28. Kuang Z.B., Yuan X.G.: Reflection and transmission theories of waves in pyroelectric and piezoelectric materials. J. Sound Vib. 330, 1111–1120 (2011)

    Article  Google Scholar 

  29. Zhou Z.D., Yang F.P., Kuang Z.B.: Reflection and transmission of plane waves at the interface of pyroelectric bi-materials. J. Sound Vib. 331, 3558–3566 (2012)

    Article  Google Scholar 

  30. Kuang Z.B.: Some thermodynamic problems in continuum mechanics. In: Piraján, J.C.M. (eds) Thermodynamics-Kinetics of Dynamic Systems, pp. 1–20. Intech Open Access Publisher, Croatia (2011)

    Google Scholar 

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

    Google Scholar 

  32. Jou, D., Casas-Vzquez, J., Lebon, G.: Extended Irreversible Thermodynamics (Third, Revised and Enlarged Edition). Springer, Berlin (2001)

  33. Kuang, Z.B.: Theory of Electroelasticity. Shanghai Jiaotong University Press, Shanghai (2011); (in Chinese)

  34. Buchen P.W.: Plane waves in linear viscoelastic media. J. R. Astron. Soc. 23(5), 531–542 (1971)

    Article  MATH  Google Scholar 

  35. Krebes E.S., Le L.H.T.: Inhomogeneous plane wave and cylindrical waves in anisotropic elastic media. J. Geophys. Res. Solid Ear. 99(B12), 23899–23919 (1994)

    Article  Google Scholar 

  36. Banerjee D.K., Bao Y.: Thermoelastic waves in anisotropic solids. J. Acoust. Soc. Am. 56(5), 1444–1454 (1974)

    Article  MATH  Google Scholar 

  37. Dieulesaint, E., Royer, D., (Eds.): Elastic Waves in Solids (A. Bastin, M. Motz, Trans.). Wiley, New York (1980)

  38. Du Q.Z., Yang H.Z.: Velocity dispersion and attenuation in anisotropic linear viscoelastic media. Acta Phys. Sin. 51(9), 2101–2108 (2002) (in Chinese)

    Google Scholar 

  39. Levin V.M., Markov M.G.: Propagation of low-frequency elastic waves in double porosity media containing viscoelastic component in the pores. Int. J. Eng. Sci. 49, 140–154 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, College of Materials, Xiamen University, Xiamen, 361005, China

    Zhi-Dong Zhou

  2. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai, 200240, China

    Feng-Peng Yang

Authors
  1. Zhi-Dong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng-Peng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Dong Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, ZD., Yang, FP. Plane waves in pyroelectrics with viscous effect. Acta Mech 225, 509–521 (2014). https://doi.org/10.1007/s00707-013-0962-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-0962-7

Keywords

Search

Navigation