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TECHNICAL PAPERS

Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates

[+] Author and Article Information
S. S. Vel, R. C. Batra

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219

J. Appl. Mech 67(3), 558-567 (Nov 23, 1999) (10 pages) doi:10.1115/1.1311274 History: Received June 02, 1999; Revised November 23, 1999
Copyright © 2000 by ASME
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References

Crawley,  E. F., and de Luis,  J., 1987, “Use of Piezoelectric Actuators as Elements of Intelligent Structures,” AIAA J., 25, pp. 1373–1385.
Im,  S., and Atluri,  S. N., 1989, “Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading,” AIAA J., 27, pp. 1801–1807.
Crawley,  E. F., and Anderson,  E. H., 1990, “Detailed Models of Piezoceramic Actuation of Beams,” J. Intell. Mater. Syst. Struct., 1, pp. 4–25.
Lee,  C. K., 1990, “Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators. Part 1: Governing Equations and Reciprocal Relationships,” J. Acoust. Soc. Am., 87, pp. 1144–1158.
Wang,  B. T., and Rogers,  C. A., 1991, “Laminate Plate Theory for Spatially Distributed Induced Strain Actuators,” J. Compos. Mater., 25, pp. 433–452.
Huang,  J. H., and Wu,  T. L., 1996, “Analysis of Hybrid Multilayered Piezoelectric Plates,” Int. J. Eng. Sci., 34, pp. 171–181.
Mitchell,  J. A., and Reddy,  J. N., 1995, “A Refined Hybrid Plate Theory for Composite Laminates With Piezoelectric Laminae,” Int. J. Solids Struct., 32, pp. 2345–2367.
Robbins,  D. H., and Reddy,  J. N., 1991, “Analysis of Piezoelectrically Actuated Beams Using a Layer-Wise Displacement Theory,” Comput. Struct., 41, pp. 265–279.
Ha,  S. K., Keilers,  C., and Chang,  F. K., 1992, “Finite Element Analysis of Composite Structures Containing Piezoceramic Sensors and Actuators,” AIAA J., 30, pp. 772–780.
Heyliger,  P., Ramirez,  G., and Saravanos,  D., 1994, “Coupled Discrete-Layer Finite Elements for Laminated Piezoelectric Plates,” Commun. Numer. Meth. Eng., 10, pp. 971–981.
Batra,  R. C., and Liang,  X. Q., 1997, “Finite Dynamic Deformations of Smart Structures,” Comput. Mech., 20, pp. 427–438.
Vlasov, B. F., 1957, “On One Case of Bending of Rectangular Thick Plates,” Vestnik Moskovskogo Universiteta. Seriëiı̀a Matematiki, mekhaniki, astronomii, fiziki, khimii, No. 2, pp. 25–34, (in Russian).
Pagano,  N. J., 1969, “Exact Solutions for Composite Laminates in Cylindrical Bending,” J. Compos. Mater., 3, pp. 398–411.
Pagano,  N. J., 1970, “Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates,” J. Compos. Mater., 4, pp. 20–34.
Srinivas,  S., and Rao,  A. K., 1970, “Bending, Vibration and Buckling of Simply Supported Thick Orthotropic Rectangular Plates and Laminates,” Int. J. Solids Struct., 6, pp. 1463–1481.
Ray,  M. C., Rao,  K. M., and Samanta,  B., 1993, “Exact Solution for Static Analysis of Intelligent Structures Under Cylindrical Bending,” Comput. Struct., 47, pp. 1031–1042.
Heyliger,  P., and Brooks,  S., 1996, “Exact Solutions for Laminated Piezoelectric Plates in Cylindrical Bending,” ASME J. Appl. Mech., 63, pp. 903–910.
Bisegna,  P., and Maceri,  F., 1996, “An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates,” ASME J. Appl. Mech., 63, pp. 628–638.
Lee,  J. S., and Jiang,  L. Z., 1996, “Exact Electroelastic Analysis of Piezoelectric Laminae via State Space Approach,” Int. J. Solids Struct., 33, pp. 977–990.
Heyliger,  P., 1994, “Static Behavior of Laminated Elastic/Piezoelectric Plates,” AIAA J., 32, pp. 2481–2484.
Heyliger,  P., 1997, “Exact Solutions for Simply Supported Laminated Piezoelectric Plates,” ASME J. Appl. Mech., 64, pp. 299–306.
Tang,  Y. Y., Noor,  A. K., and Xu,  K., 1996, “Assessment of Computational Models for Thermoelectroelastic Multilayered Plates,” Comput. Struct., 61, pp. 915–933.
Saravanos,  D. A., Heyliger,  P. R., and Hopkins,  D. A., 1997, “Layerwise Mechanics and Finite Element for the Dynamic Analysis of Piezoelectric Composite Plates,” Int. J. Solids Struct., 34, pp. 359–378.
Eshelby,  J. D., Read,  W. T., and Shockley,  W., 1953, “Anisotropic Elasticity With Applications to Dislocation Theory,” Acta Metall., 1, pp. 251–259.
Stroh,  A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3, pp. 625–646.
Ting, T. C. T., 1996, Anisotropic Elasticity. Theory and Applications, Oxford University Press, New York.
Vel,  S. S., and Batra,  R. C., 2000, “The Generalized Plane Strain Deformations of Thick Anisotropic Composite Laminated Plates,” Int. J. Solids Struct., 37, pp. 715–733.
Vel,  S. S., and Batra,  R. C., 2000, “Cylindrical Bending of Laminated Plates With Distributed and Segmented Piezoelectric Actuators/Sensors,” AIAA J., 38, pp. 857–867.
Vel,  S. S., and Batra,  R. C., 1999, “Analytical Solution for Rectangular Thick Laminated Plates Subjected to Arbitrary Boundary Conditions,” AIAA J., 37, pp. 1464–1473.
Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibrations, Plenum Press, New York.
Suo,  Z., Kuo,  C.-M., Barnett,  D. M., and Willis,  J. R., 1992, “Fracture Mechanics for Piezoelectric Ceramics,” J. Mech. Phys. Solids, 40, pp. 739–765.
Tashiro,  K., Tadokoro,  H., and Kobayashi,  M., 1981, “Structure and Piezoelectricity of Poly(Vinylidene Flouride),” Ferroelectrics, 32, pp. 167–175.
Nye, J. F., 1985, Physical Properties of Crystals, Oxford University Press, New York.
Batra,  R. C., Liang,  X. Q., and Yang,  J. S., 1996, “The Vibration of a Simply Supported Rectangular Elastic Plate Due to Piezoelectric Actuators,” Int. J. Solids Struct., 33, pp. 1597–1618.

Figures

Grahic Jump Location
An N-layer laminated piezoelectric plate
Grahic Jump Location
Influence of the boundary conditions on the through-thickness distribution of the potential due to a mechanical load for the [0 deg PVDF/90 deg PVDF] laminate
Grahic Jump Location
Influence of the boundary conditions on the through-thickness distribution of the transverse displacement, longitudinal stress, and transverse shear stress for the [0 deg PVDF/90 deg PVDF] laminate subjected to (a) mechanical load and (b) electrical load
Grahic Jump Location
Axial variation on the interface of the [0 deg PVDF/90 deg PVDF] laminate (a) transverse electric displacement for the mechanical load and (b) transverse shear stress for the electric load
Grahic Jump Location
Influence of the boundary conditions on the midplane transverse displacement of the [0 deg PVDF/90 deg PVDF] laminate for (a) mechanical load and (b) electrical load
Grahic Jump Location
Through-thickness variation of the transverse shear stress on three sections of a [0 deg PVDF/90 deg PVDF] laminate with layerwise variation of boundary conditions
Grahic Jump Location
Influence of the boundary conditions on the through-thickness distribution of the stresses for the [0 deg GE/90 deg GE/PZT-5A] laminate, (a) mechanical load and (b) electrical load
Grahic Jump Location
Axial variation of the transverse shear stress on the midsurface of the PZT-5A lamina of the [0 deg GE/90 deg GE/PZT-5A] laminate for (a) mechanical load and (b) electrical load

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