Skip to main content

Nonlinear Modeling of Piezoelectric Plates

  • Chapter
Vibrations of Elastic Plates
  • 286 Accesses

Abstract

In the three preceding chapters, we have discussed nonlinear dynamical modeling for large deflections of elastic beams, plates, and shallow shells, together with applications to nonlinear and chaotic vibrations. In this chapter, we further extend our discussion to nonlinear dynamical modeling for large deflections of piezoelectric plates.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baily, T. and J.E. Hubbard. (1987) Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam. Journal of Guidance, Control and Dynamics, Vol. 8, pp. 605–611.

    Article  Google Scholar 

  • Bugdayci, N. and D.B. Bogy. (1981) A Two-Dimensional Theory for Piezoelectric Layers Used in Electro-Mechanical Transducers—I. Derivation and II. Applications. International Journal of Solids and Structures, Vol. 17, pp. 1159–1178.

    Article  MATH  Google Scholar 

  • Bugdayci, N. and D.B. Bogy. (1981) A Two-Dimensional Theory for Piezoelectric Layers Used in Electro-Mechanical Transducers—I. Derivation and II. Applications. International Journal of Solids and Structures, Vol. 17, pp. 1179–1202.

    Article  MATH  Google Scholar 

  • Janas, V.E. and A. Safari. (1995) Overview of Fine-Scale Piezoelectric Ceramic/ Polymer Composite Processing. Journal of the American Ceramic Society, Vol. 78, pp. 2945–2955.

    Article  Google Scholar 

  • Lee, C.K. and F.C. Moon. (1990) Modal Sensors/Actuators. Journal of Applied Mechanics, Vol. 57, pp. 434–441.

    Article  Google Scholar 

  • Lee, P.C.Y., S. Syngellakis, and J.P. Hou. (1987) A Two-Dimensional Theory for High-Frequency Vibrations of Piezoelectric Crystal Plates With or Without Electrodes. Journal of Applied Physics, Vol. 61, pp. 1249–1262.

    Article  Google Scholar 

  • Mindlin, R.D. (1951a) Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates. Journal of Applied Mechanics, Vol. 18, pp. 31–38.

    MATH  Google Scholar 

  • Mindlin, R.D. (1951b) Thickness-Shear and Flexural Vibrations of Crystal Plates. Journal of Applied Physics, Vol. 22, pp. 316–323.

    Article  MathSciNet  MATH  Google Scholar 

  • Mindlin, R.D. (1952) Forced Thickness-Shear and Flexural Vibrations of Piezoelectric Crystal Plates. Journal of Applied Physics, Vol. 23, pp. 83–88.

    Article  MathSciNet  MATH  Google Scholar 

  • Mindlin, R.D. (1972) High Frequency Vibrations of Piezoelectric Crystal Plates. International Journal of Solids and Structures, Vol. 8, pp. 887–906.

    Google Scholar 

  • Mindlin, R.D. (1974) Coupled Piezoelectric Vibrations of Quartz Plates. International Journal of Solids and Structures, Vol. 10, pp. 453–459.

    Article  Google Scholar 

  • Mindlin, R.D. (1984) Frequencies of Piezoelectrically Forced Vibrations of Electroded, Doubly Rotated, Quartz Plates. International Journal of Solids and Structures, Vol. 20, pp. 141–157.

    Article  MATH  Google Scholar 

  • Newnham, R.E. and G.R. Ruschau. (1991) Smart Electroceramics. Journal of the American Ceramic Society, Vol. 74, pp. 463–480.

    Article  Google Scholar 

  • Tiersten, H.F. and R.D. Mindlin. (1962) Forced Vibrations of Piezoelectric Crystal Plates. Quarterly of Applied Mathematics, Vol. 20, pp. 107–119.

    MATH  Google Scholar 

  • Tiersten, H.F. (1969) Linear Piezoelectric Plate Vibrations. Plenum Press, New York.

    Google Scholar 

  • Toupin, R.A. (1956) The Elastic Dielectric. Journal of Rational Mechanics and Analysis, Vol. 5, pp. 849–916.

    MathSciNet  MATH  Google Scholar 

  • Tzou, H.S. (1991) Distributed Modal Identification and Vibration Control of Continua: Theory and Applications, Journal of Dynamic Systems, Measurements, and Control, Vol. 113, pp. 494–499.

    Article  Google Scholar 

  • Yu, Y.Y. (1968) Stability of Nonlinear Attitude Control Systems, Including Particularly Effect of Large Deflection of Space Vehicles. In: Proceedings of the 19th Congress of International Astronautical Federation, pp. 341–360.

    Google Scholar 

  • Yu, Y.Y. (1974) Application of Variational and Galerkin Equations to Linear and Nonlinear Finite Element Analysis. Proceedings of the 25th Congress of International Astronautical Federation, Amsterdam.

    Google Scholar 

  • Yu, Y.Y. (1992) Equations for Large Deflections of Elastic and Piezoelectric Plates and Shallow Shells, Including Sandwiches and Laminated Composites, with Applications to Vibrations, Chaos, and Acoustic Radiation. Presented at the XIIIth International Congress of Theoretical and Applied Mechanics, Haifa, Israel.

    Google Scholar 

  • Yu, Y.Y. (1995a) On Small Strains and Large Rotations in Nonlinear Elasticity and Piezoelectricity. Applied Mechanics in the Americas, Vol. I, pp. 477–482, American Academy of Mechanics and Asociacion Argentina de Mecanica Computacional, 1995.

    Google Scholar 

  • Yu, Y.Y. (1995b) On the Ordinary, Generalized, and Pseudo-Variational Equations of Motion in Nonlinear Elasticity, Piezoelectricity, and Classical Plate Theories. Journal of Applied Mechanics, Vol. 62, pp. 471–478.

    Article  MATH  Google Scholar 

  • Yu, Y.Y. (1995c) Some Recent Advances in Linear and Nonlinear Dynamical Modeling of Elastic and Piezoelectric Plates. Journal of Intelligent Material Systems and Structures, Vol. 6, pp. 237–254.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Yu, YY. (1996). Nonlinear Modeling of Piezoelectric Plates. In: Vibrations of Elastic Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2338-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2338-2_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7509-1

  • Online ISBN: 978-1-4612-2338-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics