Skip to main content
SpringerLink
Log in

Wave reflection in a rotating pyroelectric half-plane

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This paper describes the rotation effects on the wave reflection in a pyroelectric half-plane using an inhomogeneous wave approach. The rotation in the governing pyroelectric equation is characterized by considering the Coriolis and centrifugal accelerations. A scenario is modeled where a quasi-transverse wave is incident on the free boundary surface, resulting in reflected waves like temperature wave, quasi-transverse wave, quasi-longitudinal wave, and surface wave. Rotation’s effects on the reflection angle, velocity, attenuation, and energy coefficients of the reflected wave are presented.

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. Huston R.L.: Wave propagation in rotating elastic media. AIAA J. 2, 575–576 (1964)

    Article  MathSciNet  Google Scholar 

  2. Huston R.L.: In-plane vibration of spinning disks. AIAA J. 3, 1519–1520 (1965)

    Article  Google Scholar 

  3. Schoenbe M., Censor D.: Elastic-waves in rotating media. Q. Appl. Math. 31, 115–125 (1973)

    MATH  Google Scholar 

  4. Pao Y.H., Gamer U.: Acoustoelastic waves in orthotropic media. J. Acoust. Soc. Am. 77, 806–812 (1985)

    Article  MATH  Google Scholar 

  5. Destrade M., Saccomandi G.: Some results on finite amplitude elastic waves propagating in rotating media. Acta Mech. 173, 19–31 (2004)

    Article  MATH  Google Scholar 

  6. Auriault J.L.: Body wave propagation in rotating elastic media. Mech. Res. Commun. 31, 21–27 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Auriault J.-L.: Acoustics of rotating deformable saturated porous media. Transp. Porous Med. 61, 235–237 (2005)

    Article  MathSciNet  Google Scholar 

  8. Singh J., Tomar S.K.: Plane waves in a rotating micropolar porous elastic solid. J. Appl. Phys. 102, 074906–074907 (2007)

    Article  Google Scholar 

  9. Gandhi N., Michaels J.E., Lee S.J.: Acoustoelastic Lamb wave propagation in biaxially stressed plates. J. Acoust. Soc. Am. 132, 1284–1293 (2012)

    Article  Google Scholar 

  10. Destrade M.: Surface acoustic waves in rotating orthorhombic crystals. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460, 653–665 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ting T.C.T.: Surface waves in a rotating anisotropic elastic half-space. Wave Motion 40, 329–346 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Censor D., Schoenberg M.: Two dimensional wave problems in rotating elastic media. Appl. Sci. Res. 27, 401–414 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lao, B.Y.: Gyroscopic effect in surface acoustic waves. In: Ultrasonics Symposium, pp. 687–691 (1980)

  14. Yuan X.: Theory of pyroelectrics with finite wave speeds. In: Hetnarski, R. (eds) Encyclopedia of Thermal Stresses, pp. 4836–4842. Springer, Dordrecht (2014)

    Chapter  Google Scholar 

  15. Bera R.K.: Propagation of waves in random rotating infinite magneto-thermo-visco-elastic medium. Comput. Math. Appl. 36, 85–102 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wauer J.: Waves in rotating conducting piezoelectric media. J. Acoust. Soc. Am. 106, 626–636 (1999)

    Article  Google Scholar 

  17. Zhou Y.H., Jiang Q.: Effects of Coriolis force and centrifugal force on acoustic waves propagating along the surface of a piezoelectric half-space. Z. Angew. Math. Phys. 52, 950–965 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jiashi Y.: A review of analyses related to vibrations of rotating piezoelectric bodies and gyroscopes. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 698–706 (2005)

    Article  Google Scholar 

  19. Sharma J.N., Grover D.: Body wave propagation in rotating thermoelastic media. Mech. Res. Commun. 36, 715–721 (2009)

    Article  MATH  Google Scholar 

  20. Kumar R., Rupender R.: Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources. Chaos Solitons Fractals 41, 1619–1633 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Biryukov, S.V., Schmidt, H., Weihnacht, M.: Gyroscopic effect for SAW in common piezoelectric crystals. In: 2009 IEEE International Ultrasonics Symposium (IUS), pp. 2133–2136 (2009)

  22. Sharma J.N., Grover D., Kaur D.: Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids. Appl. Math. Model. 35, 3396–3407 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wegert H., Reindl L.M., Ruile W., Mayer A.P.: On the Coriolis effect in acoustic waveguides. J. Acoust. Soc. Am. 131, 3794–3801 (2012)

    Article  Google Scholar 

  24. Prasad R., Mukhopadhyay S.: Effects of rotation on harmonic plane waves under two-temperature thermoelasticity. J. Therm. Stress. 35, 1037–1055 (2012)

    Article  Google Scholar 

  25. Kothari S., Mukhopadhyay S.: Study of harmonic plane waves in rotating thermoelastic media of type III. Math. Mech. Solids 17, 824–839 (2012)

    Article  MathSciNet  Google Scholar 

  26. Abd-Alla A.M., Yahya G.A.: Thermal stresses in infinite circular cylinder subjected to rotation. Appl. Math. Mech. Engl. Ed. 33, 1059–1078 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yuan, X., Chen, S.: The inhomogeneous waves in a rotating piezoelectric body. Sci. World J. 2013, 1–8 (2013)

  28. Yuan X.: Inhomogeneous wave reflection in a rotating piezoelectric body. Acta Mech. 226, 811–827 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. Simionescu-Panait O.: Energy estimates for Love wave in a pre-stressed layered structure. Ann. Univ. Buchar (Math. Ser.) 4, 229–241 (2013)

    MathSciNet  MATH  Google Scholar 

  30. Kuang Z.-B.: Theory of Electroelasticity. Shanghai Jiao Tong University Press, Springer, Shanghai, Berlin (2014)

    Book  MATH  Google Scholar 

  31. Rahmoune, M., Essoufi, E., Sanbi, M.: Rotation and thermal effects on the rayleigh wave propagating upon a thermopiezo-electric half-space. In: The 17th International Congress on Sound and Vibration (2009)

  32. Walia V., Sharma J.N., Sharma P.K.: Propagation characteristics of thermoelastic waves in piezoelectric (6 mm class) rotating plate. Eur. J. Mech. A/Solids 28, 569–581 (2009)

    Article  MATH  Google Scholar 

  33. Yuan, X.: Effects of rotation and initial stresses on pyroelectric waves. Arch. Appl. Mech. (2015). doi:10.1007/s00419-015-1038-z

  34. Yuan X., Li L.: Waves in a rotating pyroelectric body. J. Therm. Stress. 38, 399–414 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  36. Yuan X.: The energy process of pyroelectric medium. J. Therm. Stress. 33, 413–426 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  38. Yuan X., Zhu Z.H.: Reflection and refraction of plane waves at interface between two piezoelectric media. Acta Mech. 223, 2509–2521 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Červený V.: Inhomogeneous harmonic plane waves in viscoelastic anisotropic media. Stud. Geophys. Geod. 48, 167–186 (2004)

    Article  Google Scholar 

  40. Abd-Alla A.-E.-N., Hamdan A., Giorgio I., Del Vescovo D.: The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials. Arch. Appl. Mech. 84, 1229–1248 (2014)

    Article  Google Scholar 

  41. Vernotte P.: Les paradoxes de la theorie continue de léquation de la chaleur. C. R. Acad Sci. 246, 3154 (1958)

    MathSciNet  Google Scholar 

  42. Cattaneo C.: Sur une forme de léquation eliminant le paradoxe d’une propagation instantanee. C. R. Acad Sci. 247, 431–432 (1958)

    MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  44. Abd-Alla, A.-E.-N., Giorgio, I., Galantucci, L., Hamdan, A.M., Del Vescovo, D.: Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity. Continuum Mech. Thermodyn. 1–18 (2014). doi:10.1007/s00161-014-0400-7

  45. Fedorov F.I.: Theory of Elastic Waves in Crystals. Plenum Press, New York (1968)

    Book  Google Scholar 

  46. Favretto-Cristini N., Komatitsch D., Carcione J.M., Cavallini F.: Elastic surface waves in crystals. Part 1: review of the physics. Ultrasonics 51, 653–660 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Architecture Engineering, Nantong University, Nantong, 226019, China

    Quan Jiang

  2. School of Transportation, Nantong University, Nantong, 226019, China

    Xiaoguang Yuan

Authors
  1. Quan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoguang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoguang Yuan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, Q., Yuan, X. Wave reflection in a rotating pyroelectric half-plane. Acta Mech 227, 1415–1428 (2016). https://doi.org/10.1007/s00707-015-1553-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1553-6

Keywords

Search

Navigation