Skip to main content
SpringerLink
Log in

Inhomogeneous wave reflection in a rotating piezoelectric body

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The purpose of this paper is to address the wave reflection over the rotating piezoelectric boundary surface in the framework of inhomogeneous wave theory which can introduce an additional reflected surface wave over the boundary surface to solve the problem of discrepancy between independent wave modes and boundary equations. A set of homogeneous equations in displacements and electric potential is derived within the rotatory coordinate system in the presence of the Coriolis and centrifugal acceleration presenting noticeable influence upon the wave propagation and reflection. Other than the transverse wave, the performed plane example shows that there is a critical point of when angular velocity equals the wave frequency for the quasi-longitudinal wave. The results also reveal that the angular velocity is accompanied by the modification of reflected waves especially in the case of reflected surface mode as well as the reflection angles, the amplitudes, and energy ratio coefficients.

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)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  6. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

  14. 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  MATH  MathSciNet  Google Scholar 

  15. 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 

  16. 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 

  17. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

  22. Zhou Y.H., Jiang Q.: Effects of Coriolis force and centrifugal force on acoustic waves propagating along the surface of a piezoelectric half-space. Zeitschrift für angewandte Mathematik und Physik ZAMP 52, 950–965 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  29. Goldstein, H., Poole, C.P., Safko, J.L.: Classical Mechanics, New Delhi: Pearson Education, Limited (2013)

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Henan Polytechnic University, Jiaozuo, 454000, People’s Republic of China

    Xiaoguang Yuan

Authors
  1. 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

Yuan, X. Inhomogeneous wave reflection in a rotating piezoelectric body. Acta Mech 226, 811–827 (2015). https://doi.org/10.1007/s00707-014-1225-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1225-y

Keywords

Search

Navigation