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Two-dimensional equations for high-frequency extensional vibrations of piezoelectric ceramic plates with thickness poling

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Abstract

A system of approximate, two-dimensional equations is derived for coupled extensional, thickness stretch, and symmetric thickness-shear motions of piezoelectric ceramic plates with thickness poling. Both electroded and unelectroded plates are considered. The dispersion curves for the three waves in an infinite plate determined from the derived equations are compared with analogous solutions of the three-dimensional equations with good agreement. The two-dimensional equations obtained can be used to model ceramic plate piezoelectric transducers operating with thickness stretch modes through the piezoelectric constant e 33 or in-plane extensional modes through e 31 when the plates are not very thin and edge effects as well as mode couplings cannot be neglected.

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References

  1. Meitzler, A.H., Tiersten, H.F., Warner A.W., Berlincourt, D., Couqin, G.A., Welsh, F.S. III: IEEE Standard on Piezoelectricity. IEEE, New York (1988)

  2. Mindlin, R.D.: An Introduction to the Mathematical Theory of Vibrations of Elastic Plates. In: Yang, J.S. (ed.) World Scientific, Singapore (2006)

  3. Tiersten H.F.: Thickness vibrations of piezoelectric plates. J. Acoust. Soc. Am. 35, 53–58 (1963)

    Article  MathSciNet  Google Scholar 

  4. Yang J.S.: The Mechanics of Piezoelectric Structures. World Scientific, Singapore (2006)

    Book  Google Scholar 

  5. Kane T.R., Mindlin R.D.: High-frequency extensional vibrations of plates. ASME J. Appl. Mech. 23, 277–283 (1956)

    MATH  MathSciNet  Google Scholar 

  6. Mindlin R.D., Medick M.A.: Extensional vibrations of elastic plates. ASME J. Appl. Mech. 26, 561–569 (1959)

    MathSciNet  Google Scholar 

  7. Yang, J.S., Guo, S.H.: On using the Kane–Mindlin theory in the analysis of cracks in plates. Int. J. Fracture 133, L13–L17 (2005)

  8. Tiersten, H.F.: Equations for the extension and flexure of relatively thin electrostatic plates undergoing large electric fields. In: Lee, J.S., Maugin, G.A., Shindo, Y. (eds.) Mechanics of Electromagnetic Materials and Structures, AMD Vol. 161, MD Vol. 42. ASME, New York, 21–34 (1993)

  9. Tiersten H.F.: Linear Piezoelectric Plate Vibrations. Plenum, New York (1969)

    Book  Google Scholar 

  10. Ding H.J., Chen W.Q.: Three Dimensional Problems of Piezoelasticity. Nova Science Publishers, New York (2001)

    Google Scholar 

  11. McNiven H.D., Mengi Y.: Dispersion of waves in transversely isotropic rods. J. Acoust. Soc. Am. 49, 229–236 (1971)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, Zhejiang, China

    Bin Wu & Weiqiu Chen

  2. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, USA

    Jiashi Yang

Authors
  1. Bin Wu
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  2. Weiqiu Chen
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  3. Jiashi Yang
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Correspondence to Jiashi Yang.

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Wu, B., Chen, W. & Yang, J. Two-dimensional equations for high-frequency extensional vibrations of piezoelectric ceramic plates with thickness poling. Arch Appl Mech 84, 1917–1935 (2014). https://doi.org/10.1007/s00419-014-0895-1

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  • DOI: https://doi.org/10.1007/s00419-014-0895-1

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