Acta Mechanica Solida Sinica

, Volume 28, Issue 5, pp 464–470 | Cite as

On the Interaction Between a Quartz Crystal Resonator and an Array of Micro-Beams in Thickness-Shear Vibrations

  • Lingcheng Kong
  • Xuan Xie
  • Jun Zhang
  • Yuxi Wang
  • Yuantai Hu


We studied the coupled dynamic behavior of a quartz-crystal-resonator (QCR) /micro-beams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.

Key Words

quartz crystal resonator couple stress frequency shift 


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  1. 1.
    Li, F., Wang, J.H.C. and Wang, Q.M., Thickness shear mode acoustic wave sensors for characterizing the viscoelastic properties of cell monolayer. Sens. Actuators B, 2008, 128(2): 399–406.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Munro, J.C. and Frank, C.W., Polyacryamide adsorption from aqueous solutions on gold and silver surfaces monitored by the quartz crystal microbalance. Macromolecules, 2004, 37(3): 925–938.CrossRefGoogle Scholar
  3. 3.
    Bailey, C.A., Fiebor, B., Yen, W., Vodyanoy, V., Cernosek, R.W. and Chin, B.A., Thickness shear mode (TSM) Resonators used for biosensing. Proc. SPIE, 2002, 4575: 138–149.CrossRefGoogle Scholar
  4. 4.
    Sauerbrey, G., Verwendung von schwingquarzen zur wägung dünner schichten und zur mikrowagung. Zeitschrift für Physik, 1959, 155(2): 206–222.CrossRefGoogle Scholar
  5. 5.
    Benes, E., Improved quartz crystal microbalance technique. J. Appl. Phys., 1984, 56(2): 608–626.CrossRefGoogle Scholar
  6. 6.
    Benes, E., Gröschl, M., Burger, W. and Schmid, M., Sensors based on piezoelectric resonators. Sens. Actuators A, 1995, 48: 1–21.CrossRefGoogle Scholar
  7. 7.
    EerNisse, E.P., Ward, R.W. and Wiggins, R.B., Survey of quartz bulk resonator sensor technologies. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 1988, 35(3): 323–330.CrossRefGoogle Scholar
  8. 8.
    Vig, J.R. and Ballato, A., Comments about the effects of nonuniform mass loading on a quartz crystal microbalance. IEEE Trans. Ultrason. Ferroelectr. Freq.Control, 1998, 45(5): 1123–1124.CrossRefGoogle Scholar
  9. 9.
    Zhang, L., Zhou, Z.L., Cheng, B., DeSimone, J.M. and Samulski, E.T., Superhydrophobic behavior of a perfluoropolyether lotus-leaf-like topography. Langmuir, 2006, 22(2): 8576–8580.CrossRefGoogle Scholar
  10. 10.
    Geim, A.K., Dubonos, S.V., Grigorieva, I.V., Novoselov, K. S., Zhukov, A.A. and Shapoval, S.Y., Microfabricated adhesive mimicking gecko foot-hair. Nat. Mater., 2003, 2(7): 461–463CrossRefGoogle Scholar
  11. 11.
    McAllister, D.V., Wang, P.M., Davis, S.P., Park, J.H., Canatella, P.J., Allen, M.G. and Prausnitz, M.R., Microfabricated needles for transdermal delivery of macromolecules and nanoparticles: fabrication methods and transport studies. Proc. Natl. Acad. Sci. U.S.A., 2003, 100(24): 13755–13760.CrossRefGoogle Scholar
  12. 12.
    Nomura, S., Kojima, H., Ohyabu, Y., Kuwabara, K., Miyauchi, A. and Uemura, T., Cell culture on nanopillar sheet: study of HeLa cells on nanopillar sheet. Jpn. J. Appl. Phys., 2005, 44(37): 1184–1186.CrossRefGoogle Scholar
  13. 13.
    Kim, K., Park, S., Lee, J.B., Manohara, H., Desta, Y., Murpphy, M. and Ahn, C.H., Rapid replication of polymeric and metallic high aspect ratio microstructures using PDMS and LIGA technology. Microsyst. Technol., 2002, 9(1–2): 5–10.CrossRefGoogle Scholar
  14. 14.
    Liu, N., Yang, J.S. and Wang, J., Shear vibration of a crystal plate carrying an array of microbeams. Philos. Mag. Lett., 2011, 91(9): 572–581.CrossRefGoogle Scholar
  15. 15.
    Zhang, R.Y., Xie, J.M., Hu, Y.T., Yang, J.S. and Chen, X.D., Thickness-shear vibration of an elastic plate carrying an array of rigid microbeams with consideration of couple stresses. Int. J. Eng. Sci., 2012, 51(2): 179–189.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Hu, Y.T., Hu, H.L., Luo, B., Xue, H., Xie, J.M. and Wang, J., Frequency shift of a crystal quartz resonator in thickness-shear modes induced by an array of hemispherical material units. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2013, 60: 1777–1782.CrossRefGoogle Scholar
  17. 17.
    Gere, J.M., Mechanics of Materials (5th ed.). Pacific Grove, CA: Brooks/Cole, 2001.Google Scholar
  18. 18.
    Meirovitch, L., Analytical Methods in Vibrations. New York: Macmillan, 1967.zbMATHGoogle Scholar
  19. 19.
    Mindlin, R.D. and Tiersten, H.F., Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 1962, 11: 415–448.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hu, Y.T., Cui, Z.J., Jiang, S.N. and Yang, J.S., Thickness-shear vibration of a circular crystal plate in a cylindrical shell as a pressure sensor. Applied Mathematics and Mechanics, 2006, 27(6): 749–755.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  • Lingcheng Kong
    • 1
  • Xuan Xie
    • 1
  • Jun Zhang
    • 1
  • Yuxi Wang
    • 1
  • Yuantai Hu
    • 1
  1. 1.Department of MechanicsHuazhong University of science and TechnologyWuhanChina

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