Common Piezoelectric Continua and Active Piezoelectric Structures

  • Hornsen (HS) TzouEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 247)


In this chapter, applications of the generic piezoelectric shell theories to a number of common piezoelectric continua were presented. A four-step reduction procedure was introduced and it was demonstrated in two geometries. The first case was a piezoelectric plate which includes 1) a thick plate and 2) a thin plate. The derived system equations of the thick piezoelectric plate were completely identical to published results (Tiersten, 1969). The second case was a piezoelectric shell of revolution which represents another class of shell continua e.g., piezoelectric spheres, cylinders, cones, etc., which were discussed in detail. Applications of the generic shell vibration theory to other piezoelectric continua can be further explored. Note that the theory was derived based on a symmetrical hexagonal piezoelectric structure—class \({\text{C}}_{6{\text{v}}} = 6\, {\text{mm}}\).


  1. Soedel, W., 1981, Vibrations of Shells and Plates, Dekker, New York.Google Scholar
  2. Thomson, W.T., 1981, Theory of Vibration with Applications, Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  3. Tiersten, H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum Press, New York.Google Scholar
  4. Tzou, H.S. and Pandita, S., 1987, “A Multi-Purpose Dynamic and Tactile Sensor for Robot Manipulators,” (with Pandita, S.), Journal of Robotic Systems, Vol. (4.6), pp. 719–741, 1987.CrossRefGoogle Scholar
  5. Tzou, H.S., 1989, “Integrated Distributed Sensing and Active Vibration Suppression of Flexible Manipulators using Distributed Piezoelectrics,” Journal of Robotic Systems, Vol.(6), No.6, pp.745–767, December 1989.Google Scholar
  6. Tzou, H.S., 1992, “A New Distributed Sensation and Control Theory for “Intelligent” Shells,” Journal of Sound and Vibration, Vol.152, No.3, pp.335–350, March 1992.CrossRefGoogle Scholar
  7. Tzou, H.S. and Zhong, J.P., 1990, “Electromechanical Dynamics of Piezoelectric Shell Distributed Systems, Part-1&2,” Robotics Research-1990, ASME-DSC-Vol.26, pp. 207–211, 1990 ASME Winter Annual Meetings, Dallas, Texas, Nov. 25–30, 1990; “Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems,” ASME Journal of Dynamic Systems, Measurements, and Control, 1993.Google Scholar
  8. Tzou, H.S. and Zhong, J.P., 1991a, “Adaptive Piezoelectric Shell Structures: Theory and Experiments,” AIAA/ASME/ASCE/AHA/ASC 32nd Structures, Structural Dynamics and Materials Conference, pp. 2290–2296, Paper No. AIAA-91-1238-CP, Baltimore, Maryland, April 8–10, 1991. Mechanical Systems and Signal Processing, Vol. (7), No. (3), May 1993.Google Scholar
  9. Tzou, H.S. and Zhong, J.P., 1991b, “Control of Piezoelectric Cylindrical Shells via Distributed In-Plane Membrane Forces,” Controls for Aerospace Systems, DSC-Vol.35, pp. 15–20, Distributed Control of Flexible Structures, Aerospace Panel, Dynamic Systems and Control Division, 1991 ASME WAM, Atlanta, GA, December 1–6, 1991.Google Scholar
  10. Tzou, H.S. and Zhong, J.P., 1991c, “Theory on Hexagonal Symmetrical Piezoelectric Thick Shells Applied to Smart Structures,” Structural Vibration and Acoustics, Edrs. Huang, Tzou, et al., ASME-DE-Vol.34, pp. 7–15, Symposium on Intelligent Structural Systems, 1991 ASME 13th Biennial Conference on Mechanical Vibration and Noise, Miami, Florida, September 22–25, 1991.Google Scholar
  11. Tzou, H.S., 1992, “Active Piezoelectric Shell Continua,” Intelligent Structural Systems, H.S. Tzou & G.L. Anderson, (Editors), pp. 9–74, Kluwer Academic Publishers, Aug. 1992.Google Scholar
  12. Tzou, H.S., 2000, “Integrated Piezoelectric Sensor Actuator Design for Distributed Identification and Control of “Smart” Machines and Flexible Robots: Part 1: Theory and Experiments,” Intelligent Systems and Robotics, G.W. Zobrist and C.Y Ho, (Editors), pp. 92–122, Gordon and Breach Science Publishers (2000OPA), Netherlands, 2000.Google Scholar
  13. Tzou, H.S., Zhu, Y.T. and Hagiwara, I., 2002, “Distributed Precision Control of Structronic Shells and Common Shapes – A New Approach,” Recent Research Developments in Sound & Vibration, ISBN: 81-7895-031-6, Vol.1, Part-2, pp. 613–646, TransWorld Research, 2002.Google Scholar
  14. Zhong, J.P., 1991, A Study of Piezoelectric Shell Dynamics Applied to DIstributed Structural Identification and Control, Ph.D. Thesis, Department of Mechanical Engineering, University of Kentucky, Lexington, KY. (3/PzShl.BkPzSm1).Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical Structures; Interdisciplinary Research Institute, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

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