Acta Mechanica

, Volume 228, Issue 5, pp 1891–1907 | Cite as

Inhomogeneous waves in porous piezo-thermoelastic solids

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Abstract

A mathematical model for taking into consideration the interaction of mechanical, thermal and electrical dynamics in an anisotropic porous piezo-thermoelastic (APPT) medium is presented. Basic equations for APPT are derived. The three-dimensional problem of wave propagation is studied which explains the existence and propagation of six waves in the considered medium. The phase velocities and attenuation factors for each of the six attenuated waves are determined in terms of complex slowness vectors. The particular results are obtained for triclinic, monoclinic and orthotropic types of crystal symmetries. The effects of piezoelectricity, thermoelasticity, frequency, and porosity on the wave propagation phenomenon are analyzed.

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References

  1. 1.
    Harvey, J.A.: Kirk-Othmer Encyclopedia of Chemical Technology, 4th Ed., supplement, pp. 502–504. Wiley, New York (1998)Google Scholar
  2. 2.
    Yu, J.G., Zhang, B., Lefebvre, J.E., Zhang, C.H.: Wave propagation in functionally graded piezoelectric rods with rectangular cross-section. Arch. Mech. 67, 213–231 (2015)MathSciNetMATHGoogle Scholar
  3. 3.
    Fung, R.F., Huang, J.S., Jan, S.C.: Dynamic analysis of a piezothermoelastic resonator with various shapes. J. Vib. Acoust. 122, 244–253 (2000)CrossRefGoogle Scholar
  4. 4.
    Barati, A.R., Jabbari, M.: Two-dimensional piezothermoelastic analysis of a smart FGM hollow sphere. Acta Mech. 226, 2195–2224 (2015)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Mindlin, R.D.: On the equations of motion of piezoelectric crystals, Problems of Continuum Mechanics (N. I. Muskhelishvili 70th Birthday Volume), 282 (1961)Google Scholar
  6. 6.
    Mindlin, R.D.: Equations of high frequency vibrations of thermopiezoelectric crystal plates. Int. J. Solids Struct. 10, 625–637 (1974)CrossRefMATHGoogle Scholar
  7. 7.
    Nowacki, W.: Some general theorems of thermopiezoelectricity. J. Therm. Stress. 1, 171–182 (1978)CrossRefGoogle Scholar
  8. 8.
    Chandrasekharaiah, D.S.: A temperature rate dependent theory of piezoelectricity. J. Therm. Stress. 7, 293–306 (1984)CrossRefGoogle Scholar
  9. 9.
    Tauchert, T.R.: Piezothermoelastic behaviour of plate of crystal class 6mm a laminated plate. J. Therm. Stress. 15, 25–37 (1992)CrossRefGoogle Scholar
  10. 10.
    Yang, J.S., Batra, R.C.: Free vibrations of a linear thermopiezoelectric body. J. Therm. Stress. 18, 247–262 (1995)CrossRefGoogle Scholar
  11. 11.
    Biot, M.A.: Theory of propagation of elastic waves in fluid saturated porous solid. I. Low frequency range. J. Acoust. Soc. Am. 28, 168–178 (1956)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Biot, M.A.: Theory of propagation of elastic waves in fluid saturated porous solid. I. High frequency range. J. Acoust. Soc. Am. 28, 179–191 (1956)CrossRefGoogle Scholar
  13. 13.
    Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240–253 (1956)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sharma, M.D.: Wave propagation in thermoelastic saturated porous medium. J. Earth Syst. Sci. 117, 951–958 (2008)CrossRefGoogle Scholar
  15. 15.
    Pecker, C., Deresiewicz, H.: Thermal effects on wave propagation in liquid-filled porous media. Acta Mech. 16, 45–64 (1973)CrossRefGoogle Scholar
  16. 16.
    Youseff, H.M.: Theory of generalized porothermoelasticity. Int. J. Rock Mech. Mining Sci. 44, 222–227 (2007)CrossRefGoogle Scholar
  17. 17.
    Wersing, W., Lubitz, K., Moliaupt, J.: Dielectric elastic and piezoelectric properties of porous PZT ceramics. Ferroelectrics 68, 77–97 (1986)CrossRefGoogle Scholar
  18. 18.
    Dunn, H., Taya, M.: Electromechanical properties of porous piezoelectric ceramics. J. Am. Cer. Soc. 76, 1697–1706 (1993)CrossRefGoogle Scholar
  19. 19.
    Vashishth, A.K., Gupta, V.: Vibrations of porous piezoelectric ceramic plates. J. Sound Vib. 325, 781–797 (2009)CrossRefGoogle Scholar
  20. 20.
    Sharma, M.D.: Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium. Proc. R. Soc. A. 466, 1977–1992 (2010)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Ciarletta, M., Scalia, A.: Thermodynamic theory for porous piezoelectric materials. Meccanica 28, 303–308 (1993)CrossRefMATHGoogle Scholar
  22. 22.
    Ciarletta, M., Scarpetta, E.: Some results on thermoelasticity for porous-piezoelectric materials. Mech. Res. Comm. 23, 1–10 (1996)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Jabbari, M., Yooshi, Y.: Theory of generalized piezoporo thermoelasticity. J. Solid Mech. 4, 327–338 (2012)Google Scholar
  24. 24.
    Simionescu-Panait, O., Harabagiu, L.: Propagation of inhomogeneous waves in monoclinic crystals subject to initial fields. Balkan J. Geom. Appl. 20(1), 109–119 (2015)MathSciNetMATHGoogle Scholar
  25. 25.
    Hayes, M.: Energy flux for trains of inhomogeneous plane waves. Proc. R. Soc. Lond. Ser. A. 370, 417–429 (1980)CrossRefMATHGoogle Scholar
  26. 26.
    Caviglia, G., Morro, A.: Inhomogeneous Waves in Solids and Fluids. World Scientific, Singapore (1992)CrossRefMATHGoogle Scholar
  27. 27.
    Carcione, J.M.: Wave fields in real media: wave propagation in anisotropic, anelastic and porous media. Pergamon, Amsterdam (2001)Google Scholar
  28. 28.
    Cerveny, V., Psencik, I.: Plane waves in viscoelastic anisotropic media-I. Theory. Geophys. J. Int. 161, 197–212 (2005)CrossRefGoogle Scholar
  29. 29.
    Sharma, M.D.: Propagation of inhomogeneous waves in a generalized thermoelastic anisotropic medium. J. Therm. Stress. 30, 679–691 (2007)CrossRefGoogle Scholar
  30. 30.
    Sharma, M.D.: Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium. Int. J. Solids. Struct. 45, 1483–1496 (2008)CrossRefMATHGoogle Scholar
  31. 31.
    Scott, N.H.: Energy and dissipation of inhomogeneous plane waves in thermoelasticity. Wave Motion 23, 393–406 (1996)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Sharma, M.D.: Propagation of inhomogeneous waves in anisotropic piezothermoelastic media. Acta Mech. 215, 307–318 (2010)CrossRefMATHGoogle Scholar
  33. 33.
    Vashishth, A.K., Sukhija, H.: Inhomogeneous waves at the boundary of an anisotropic piezo-thermoelastic medium. Acta Mech. 225, 3325–3338 (2014)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Declercq, Nico F., Degrieck, J., Leroy, O.: Inhomogeneous waves in piezoelectric crystals. Acta Acust. United Acust. 91, 840–845 (2005)MATHGoogle Scholar
  35. 35.
    Haertling, G.H.: Ferroelectric ceramics: history and technology. J. Am. Cer. Soc. 82, 797–818 (1999)CrossRefGoogle Scholar
  36. 36.
    Biot, M.A.: Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys. 33, 1482–1498 (1962)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Sharma, M.D.: Three-dimensional wave propagation in a general anisotropic poroelastic medium: phase velocity, group velocity and polarization. Geophys. J. Int. 156, 329–344 (2004)CrossRefGoogle Scholar
  38. 38.
    Borcherdt, R.D.: Reflection-refraction of general P and type-I S waves in elastic and anelastic solids. Geophys. J. R. Astr. Soc. 70, 621–638 (1982)CrossRefMATHGoogle Scholar
  39. 39.
    Vashishth, A.K., Gupta, V.: 3-D waves in porous piezoelectric materials. Mech. Mater. 80, 96–112 (2015)CrossRefGoogle Scholar
  40. 40.
    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)CrossRefGoogle Scholar
  41. 41.
    Craciun, F., Guidarelli, G., Galassi, C., Roncari, E.: Elastic wave propagation in porous piezoelectric ceramics. Ultrasonics. 36, 427–430 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Department of MathematicsKurukshetra UniversityKurukshetraIndia

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