Piezoelectric Shell Vibrations

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


Active piezoelectric structures capable of self-adaptation (Tzou & Anderson, 1992) and high-precision manipulations (Tzou & Fukuda, 1992).


  1. Adelman, N. T. and Stavsky, Y., 1975a, “Vibrations of Radially Polarized Composite Piezoelectric Cylinders and Disks,” J. Sound and Vibration, 37-44, 1975.Google Scholar
  2. Adelman, N. T. and Stavsky, Y., 1975b, “Axisymmetric Vibrations of Radially Polarized Piezoelectric Ceramic Cylinders,” J. Sound and Vibration, 38(2), 245-254, 1975.CrossRefGoogle Scholar
  3. Bleustain, J. L., 1969, “Some Simple Modes of Wave Propagation in an Infinite Piezoelectric Plate,” J. Acoust. Soc. Am. 45, 00.614-620, 1969.Google Scholar
  4. Cady, W. G., 1946, Piezoelectricity, McGraw?Hill, New York, 1946.Google Scholar
  5. Chau, L. K., 1986, “The Theory of Piezoelectric Shells,” PMM U.S.S.R., Vol. 50, No. 1, 98-105, 1986.Google Scholar
  6. Dökmeci, M. C., 1978, “Theory of Vibrations of Coated, Thermopiezoelectric Laminae,” J. Math. Phys., Vol. 19, No. 1, January 1978.CrossRefGoogle Scholar
  7. Dökmeci, M. C., 1980, “Vibrations of Piezoelectric Crystals,” J. Eng. Soc. Vol. 18, 431-448, 1980.CrossRefGoogle Scholar
  8. Drumheller, D. S. and Kalnins, A., 1970, “Dynamic Shell Theroy for Ferroelectric Ceramics,” J. Acoust. Soc. Am. 47, 1343, 1970.Google Scholar
  9. Eer Nisse, E. P., 1966, “Coupled?Mode Approach to Elastic Vibration Analysis,” J. Acoust. Soc. Am. 40, pp.1045-1055, 1966.Google Scholar
  10. Haskins, J. F. and Walsh, 1957, “Vibration of Ferroelectric Cylindrical Shells with Transverse Isotropy,” J. L., J. Acoust. Soc. Am. 29, 729-734, 1957.Google Scholar
  11. Holland, R. and Eer Nisse, E. P., 1969, Design of Resonant Piezoelectric Devices, M.I.T. Press, Cambridge, Massachusetts, 1969.Google Scholar
  12. Holland, R, “Resonant Properties of Piezoelectric Ceramic Rectangular Parallelepipeds,” J. Acoust. Soc. Am. 43, pp.988-997, 1968.CrossRefGoogle Scholar
  13. Kagawa, Y. and Yamabuchi, T., 1976, “A Finite Element Appraoch to Electromechanical Problems with an Application to Energy?Trapped and Suface?Wave Divices,” IEEE Trans. Sonics Ultrason., SU-23, pp.263-272, 1976.Google Scholar
  14. Keuning, D. H., 1972, “Exact Resonant Frequencies for the Thickness?Twist Trapped Energy Mode in a Piezoceramic Plate,” J. Eng. Math. 6, pp.143-154, 1972.CrossRefGoogle Scholar
  15. Mason, W. P., Piezoelectric Crystals and Their Applications to Ultrasonics, Van Nostrand, New York, 1950.Google Scholar
  16. Mindlin, R. D., 1955, An Introduction to the Mathematical Theory of Vibrations of Elastic Plates, U.S. Army Signal Corps Engineering Laboratories, Fort Monmouth, New Jersey.Google Scholar
  17. Paul, H. S., 1968, “Vibrational Waves in a Thick Infinite Plate of Piezoelectric Crystal,” J. Acoust. Soc. Am. 44, pp.478-482, 1968.CrossRefGoogle Scholar
  18. Paul, H. S., 1978, “Vibrations of a Hollow Circular Cylinder of Piezoelectric Ceramics,” J. Acoust. Soc. Am. 82(3), September 1978.CrossRefGoogle Scholar
  19. Paul, H. S., 1982, “Asymptotic Analysis of the Modes of Wave Propagation in a Piezoelectric Solid Cylinder,” J. Acoust. Soc. Am. 71(2), February 1982.Google Scholar
  20. Paul, H. S., 1986, “Axisymmetric Vibration of a Piezoelectric Solid Cylinder Guided by a Thin Film,” J. Acoust. Soc. Am. 80(4), October 1986.CrossRefGoogle Scholar
  21. Paul, H. S., 1987, “Wave Propagation in a Piezoelectric Solid Cylinder of Arbitrary Cross Section,” J. Acoust. Soc. Am. 82(6), December 1987.CrossRefGoogle Scholar
  22. Rogacheva, N. N., 1982, “Equations of State of Piezoceramic Shells,” PMM U.S.S.R., Vol. 45, 677-684, 1982.CrossRefGoogle Scholar
  23. Rogacheva, N. N., 1984a, “On Boundary conditions in the Theory of Piezoceramic Shells Polarized Along Coordinate Lines,” PMM U.S.S.R., Vol. 47, No. 2, 220-226, 1984.MathSciNetCrossRefGoogle Scholar
  24. Rogacheva, N. N., 1984b, “On Stain?Venant Type Conditions in the Theory of Piezoelastic Shells,” PMM U.S.S.R., Vol. 48, No. 2, 213-216, 1984.Google Scholar
  25. Rogacheva, N. N., 1986, “Classification of Free Piezoceramic Shell Vibrations,” PMM U.S.S.R., Vol. 50, No. 1,106-111, 1986.MathSciNetCrossRefGoogle Scholar
  26. Schmidt, G. H., 1972, “Extensional Vibrations of Piezoelectric Plates,” J. Eng. Math. 6, pp.133-142, 1972.CrossRefGoogle Scholar
  27. Senik, N. A. and Kudriavtsev, B. A., 1980, “Equations on the Theory of Piezoceramic Shells,” In: Mechanics of a solid deformable body and related analytical problems. Moscow, Izd. mosk. Inst. Chim. Mashinostroeniia, 1980.Google Scholar
  28. Soedel, W., 1981, Vibrations of Shells and Plates, Marcel Dekker, Inc., New York, 1981.Google Scholar
  29. Tiersten, H. F. and Mindlin, R.D., 1962, Appl. Math. 20, 107-109, 1962.Google Scholar
  30. Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York, 1969.Google Scholar
  31. Toupin, R. A., 1959, “Piezoelectric Relation and the Rachial Deformation of Polarized Spherical Shell,” J. Acoust. Soc. Am. 31, 315-318, 1959.Google Scholar
  32. Tzou, H.S., 1991, “Distributed Modal Identification and Vibration Control of Continua: Theory and Applications,” ASME Journal of Dynamic Systems, Measurements, and Control, Vol.(133), No.(3), 1991.Google Scholar
  33. 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.Google Scholar
  34. Tzou, H.S. and Anderson, G.L. (Editors), Intelligent Structural Systems, ISBN No.0-7923-1920-6, 488 pages, Book, Kluwer Academic Publishers, August 1992.Google Scholar
  35. Tzou, H.S., and Gadre, M, 1989, “Theoretical Analysis of a Multi-Layered Thin Shell Coupled with Piezoelectric Shell Actuators for Distributed Vibration Control,” Journal of Sound and Vibration, Vol.132, No.3, pp.433-450, August 1989.CrossRefGoogle Scholar
  36. 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; ASME Journal of Dynamic Systems, Measurements, and Control.Google Scholar
  37. 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
  38. Tzou, H.S. and Zhong, J.P., 1991b, “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
  39. Tzou, H.S., Zhong, J.P., and Natori, M.C., 1993, “Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” ASME Transactions, Journal of Vibration & Acoustics, Vol.115, No.1, pp.40 46, January 1993.CrossRefGoogle Scholar
  40. Tzou, H.S. and Zhong, J.P., 1991d, “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
  41. 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
  42. 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
  43. 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
  44. Tzou, H.S. and Fukuda, T. (Editors), Precision Sensors, Actuators, and Systems, ISBN 0-7923-2015-8, 478 pages, Book, Kluwer Academic Publishers, Dordrecht/Boston/London, December 1992; April 2002 (2nd print).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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