Skip to main content
Log in

Thickness-shear vibration of circular crystal plate in cylindrical shell as pressure sensor

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Based on the theory for small fields superposed on relatively larger fields in an electroelastic body, a theoretical analysis is performed on a circular plate thickness-shear crystal resonator sealed in a circular cylindrical shell for pressure measurement. A simple expression is obtained for pressure induced frequency shifts in the resonator, which is examined for design optimization. Numerical results show that the frequency shifts depend linearly on the pressure, and that a pressure sensor with a softer outer shell or a smaller thickness ratio of the crystal plate to the outer shell has higher sensitivity.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baumhauer J C, Tiersten H F. Nonlinear electroelastic equations for small fields superposed on a bias[J]. J Acoust Soc Amer, 1973, 54(4):1017–1034.

    Article  MATH  Google Scholar 

  2. Tiersten H F. On the accurate description of piezoelectric resonators subject to biasing deformations[J]. Internat J Engng Sci, 1995, 33(15):2239–2259.

    Article  MATH  MathSciNet  Google Scholar 

  3. Tiersten H F. Nonlinear electroelastic equations cubic in the small field variables[J]. J Acoust Soc Amer, 1975, 57(3):660–666.

    Article  MATH  Google Scholar 

  4. Besson R J, Boy J J, Glotin B, Jinzaki Y, Sinha B. A dual-mode thickness-shear quartz pressure sensor[J]. IEEE Trans on Ultrasonics, Ferroelectrics, and Frequency Control, 1993, 40(4):584–591.

    Article  Google Scholar 

  5. EerNisse E P, Wiggins R B. Review of thickness-shear mode quartz resonator sensors for temperature and pressure[J]. IEEE Sensors Journal, 2001, 1(1):79–87.

    Article  Google Scholar 

  6. EerNisse E P. Quartz resonators vs their environment: time base or sensor?[J]. J Appl Phys, 2001, 40(5):3479–3483.

    Google Scholar 

  7. Yang Jiashi, Hu Yuantai. Mechanics of electroelastic bodies under biasing fields[J]. Applied Mechanics Reviews, 2004, 57(3):173–189.

    Article  Google Scholar 

  8. Tiersten H F, Zhou Y S. An analysis of transversely varying thickness modes in quartz resonators with bevelled cylindrical edges[C]. In: Proc1993 IEEE Internat Frequency Control Symp. IEEE Press, Piscataway, NJ, USA, 1993, 431–441.

    Google Scholar 

  9. Tiersten H F. Perturbation theory for linear electroelastic equations for small fields superposed on a bias[J]. J Acoust Soc Amer, 1978, 64(3):832–837.

    Article  MATH  Google Scholar 

  10. Yang Jiashi. An Introduction to the Theory of Piezoelectricity[M]. Springer, New York, 2005, 287–297.

    Google Scholar 

  11. Hu Yuantai, Yang Jiashi, Jiang Qing. A model for electroelastic plates under biasing fields with applications in buckling analysis[J]. Internat J Sol Struct, 2002, 39(9):2629–2642.

    Article  MATH  Google Scholar 

  12. Hu Yuantai, Yang Jiashi, Jiang Qing. Surface waves in electroelastic materials under biasing fields[J]. ZAMP, 2004, 55(4):678–700.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hu Yuantai, Yang Jiashi, Jiang Qing. On modeling of extension and flexure response of electroelastic shells under biasing fields[J]. Acta Mechanica, 2002, 156(3/4):163–178.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cui Zhi-jian  (崔之键).

Additional information

Communicated by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (No.10172036) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (SRF for ROCS, SEM).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, Yt., Cui, Zj., Jiang, Sn. et al. Thickness-shear vibration of circular crystal plate in cylindrical shell as pressure sensor. Appl Math Mech 27, 749–755 (2006). https://doi.org/10.1007/s10483-006-0605-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0605-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Navigation