Advertisement

Extension and Bending of Plates

  • Jiashi Yang
Chapter
  • 30 Downloads

Abstract

In addition to beams or fibers, piezoelectric semiconductor plates or thin films are also widely used in devices in extension and bending. In this chapter, we derive two-dimensional equations for thin plates of piezoelectric semiconductors [1, 2]. We follow R.D. Mindlin’s approach [3–5], beginning from the three-dimensional equations with power series expansions in the plate thickness coordinate and then truncating the expansions to obtain low-order equations for extension and/or bending. The last section is on shells.

Keywords

Plate Film Two-dimensional model Power series Zero-order First-order Stress relaxation Extension Bending Shear deformation Thickness shear Thickness vibration Correction factor Shell Membrane theory 

References

  1. 1.
    J.S. Yang, H.G. Zhou, Amplification of acoustic waves in piezoelectric semiconductor plates. Int. J. Solids Struct. 42, 3171–3183 (2005)CrossRefGoogle Scholar
  2. 2.
    Y.X. Luo, C.L. Zhang, W.Q. Chen, J.S. Yang, Piezotronic effect of a thin film with elastic and piezoelectric semiconductor layers under a static flexural loading. ASME J. Appl. Mech. 86, 051003 (2019)ADSCrossRefGoogle Scholar
  3. 3.
    R.D. Mindlin, in An Introduction to the Mathematical Theory of Vibrations of Elastic Plates, ed. by J.S. Yang, (World Scientific, Singapore, 2006)CrossRefGoogle Scholar
  4. 4.
    R.D. Mindlin, High frequency vibrations of crystal plates. Q. Appl. Math. 19, 51–61 (1961)CrossRefGoogle Scholar
  5. 5.
    R.D. Mindlin, High frequency vibrations of piezoelectric crystal plates. Int. J. Solids Struct. 8, 895–906 (1972)CrossRefGoogle Scholar
  6. 6.
    J.S. Yang, The Mechanics of Piezoelectric Structures (World Scientific, Singapore, 2006)CrossRefGoogle Scholar
  7. 7.
    J.L. Bleustein, H.F. Tiersten, Forced thickness-shear vibrations of discontinuously plated piezoelectric plates. J. Acoust. Soc. Am. 43, 1311–1318 (1968)ADSCrossRefGoogle Scholar
  8. 8.
    J.S. Yang, X.M. Yang, J.A. Turner, Amplification of acoustic waves in piezoelectric semiconductor shells. J. Intell. Mater. Syst. Struct. 16, 613–621 (2005)CrossRefGoogle Scholar
  9. 9.
    H. Kraus, Thin Elastic Shells (Wiley, New York, 1967)zbMATHGoogle Scholar
  10. 10.
    H.S. Tzou, Piezoelectric Shells (Kluwer, Dordrecht, 1993)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Jiashi Yang
    • 1
  1. 1.LincolnUSA

Personalised recommendations