Linear Theory of Piezoelectricity

  • Jiashi Yang
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 9)


In this chapter we specialize on the nonlinear equations in Chap.  1 for large deformations and strong fields to the case of infinitesimal deformations and weak fields, which results in the linear theory of piezoelectricity. A few theoretical aspects of the linear theory are also discussed.


Linearization Superposition Poynting’s theorem Uniqueness Variational principle Matrix notation 


  1. 1.
    H.F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969)Google Scholar
  2. 2.
    A.H. Meitzler, H.F. Tiersten, A.W. Warner, D. Berlincourt, G.A. Couqin, F.S. Welsh III, IEEE Standard on Piezoelectricity (IEEE, New York, 1988)Google Scholar
  3. 3.
    Q.H. Du, S.W. Yu, Z.H. Yao, Theory of Elasticity (Science Press, Beijing, 1986)Google Scholar
  4. 4.
    H.-L. Zhang, On variational principles of a piezoelectric body. Acta Acustica 10, 223–230 (1985)Google Scholar
  5. 5.
    J. S. Yang, Mixed variational principles for piezoelectric elasticity, in: Developments in Theoretical and Applied Mechanics (Proc. of the 16th Southeastern Conference on Theoretical and Applied Mechanics), B. Antar, R. Engels, A. A. Prinaris and T. H. Moulden, ed., vol. XVI, pp. II.1.31–38, The University of Tennessee Space Institute, 1992Google Scholar
  6. 6.
    R. Holland, E.P. EerNisse, Design of Resonant Piezoelectric Devices (MIT Press, Cambridge, MA, 1969)Google Scholar
  7. 7.
    V.V. Varadan, J.-H. Jeng, V.K. Varadan, Form invariant constitutive relations for transversely isotropic piezoelectric materials. J. Acoust. Soc. Am. 82, 337–341 (1987)CrossRefGoogle Scholar
  8. 8.
    G.F. Smith, M.M. Smith, R.S. Rivlin, Integrity bases for a symmetric tensor and a vector-the crystal classes. Arch. Rat. Mech. Anal. 12, 93–133 (1963)CrossRefGoogle Scholar
  9. 9.
    B.A. Auld, Acoustic Fields and Waves in Solids, vol 1 (Wiley, New York, 1973)Google Scholar
  10. 10.
    J.L. Bleustein, A new surface wave in piezoelectric materials. Appl. Phys. Lett. 13, 412–413 (1968)CrossRefGoogle Scholar
  11. 11.
    V.E. Bottom, Introduction to Quartz Crystal Unit Design (Van Nostrand Reinhold, New York, 1982)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jiashi Yang
    • 1
  1. 1.Department of Mechanical and Materials EngineeringUniversity of Nebraska-LincolnLincolnUSA

Personalised recommendations