Two-Dimensional Piezoelasticity and Zigzag Theory Solutions for Vibration of Initially Stressed Hybrid Beams

[+] Author and Article Information
S. Kapuria, N. Alam, N. K. Jain

Applied Mechanics Department, Indian Institute of Technology Delhi, New Delhi 110016, India

J. Vib. Acoust 127(2), 116-124 (May 03, 2005) (9 pages) doi:10.1115/1.1857923 History: Received August 19, 2003; Revised January 21, 2004; Online May 03, 2005
Copyright © 2005 by ASME
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Tauchert,  T. R., 1991, “Thermally Induced Flexure, Buckling and Vibration of Plates,” Appl. Mech. Rev., 44, pp. 347–360.
Noor,  A. K., and Burton,  W. S., 1992, “Computational Models for High Temperature Multilayered Composite Plate and Shells,” Appl. Mech. Rev., 45, pp. 414–446.
Yu, Y. Y., 1996, Vibration of Elastic Plates: Linear and Nonlinear Dynamical Modelling of Sandwiches, Laminated Composites and Piezoelectric Layers, Springer, Berlin/New York.
Noor,  A. K., and Burton,  W. S., 1992, “Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates,” ASME J. Appl. Mech., 59, pp. 868–877.
Noor,  A. K., Peters,  J. M., and Burton,  W. S., 1994, “Three-Dimensional Solutions for Initially Stressed Structural Sandwiches,” J. Eng. Mech., 120, pp. 284–303.
Biot,  M. A., 1974, “Buckling and Dynamics of Multilayered and Laminated Plates Under Initial Stress,” Int. J. Solids Struct., 10, pp. 419–451.
Sun,  C. T., and Whitney,  J. M., 1976, “Dynamic Response of Laminated Composite Plates Under Initial Stress,” AIAA J., 14, pp. 268–270.
Dhanaraj,  R., 1990, “Free Vibration of Initially Stressed Composite Laminates,” J. Sound Vib., 142, pp. 365–378.
Yang,  I. H., and Kuo,  W. S., 1993, “Stability and Vibration of Initially Stressed Thick Laminated Plates,” J. Sound Vib., 168, pp. 285–297.
Kuo,  W. S., and Huang,  J. H., 1997, “Stability and Vibration of Initially Stressed Plates Composed of Spatially Distributed Fiber Composites,” J. Sound Vib., 199, pp. 51–69.
Matsunaga,  H., 2002, “Vibration of Cross-Ply Laminated Composite Plates Subjected to Initial In-Plane Stresses,” Thin-Walled Struct., 40, pp. 557–571.
Librescu,  L., and Chang,  M. Y., 1992, “Vibration of Compressively Loaded Shear Deformable Flat Panels Exhibiting Geometric Imperfections,” AIAA J., 30, pp. 2793–2795.
Librescu,  L., and Chang,  M. Y., 1993, “Effects of Geometric Imperfections on Vibration of Compressed Shear Deformable Laminated Composite Curved Panels,” Acta Mech., 96, pp. 203–224.
Librescu,  L., Lin,  W., Nemeth,  M. P., and Starnes,  J. H., 1996, “Frequency-Load Interaction of Geometrically Imperfect Curved Panels Subjected to Heating,” AIAA J., 34, pp. 166–177.
Yang,  J., 2001, “Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates,” Compos. Struct., 54, pp. 497–508.
Xu,  K., Noor,  A. K., and Tang,  Y. Y., 1997, “Three-Dimensional Solutions for Free Vibrations of Initially-Stressed Thermoelectroelastic Multilayered Plates,” Comput. Methods Appl. Mech. Eng., 141, pp. 125–139.
Pai,  P. F., Nafeh,  A. H., Oh,  K., and Mook,  D. T., 1993, “A Refined Nonlinear Model of Composite Plates With Integrated Piezoelectric Actuators and Sensors,” Int. J. Solids Struct., 30, pp. 1603–1630.
Tzou,  H. S., and Zhou,  Y. H., 1995, “Dynamics and Control of Nonlinear Circular Plates With Piezoelectric Actuators,” J. Sound Vib., 188, 189–207.
Bao,  Y., Tzou,  H. S., and Venkayya,  V. B., 1998, “Analysis of Non-Linear Piezothermoelastic Laminated Beams With Electric and Temperature Effects,” J. Sound Vib., 209, pp. 505–518.
Hermandes,  J. A., Almeida,  S. F. M., and Nabarrete,  A., 2000, “Stiffening Effects on the Free Vibration Behavior of Composite Plates With Pzt Actuators,” Compos. Struct., 49, pp. 55–63.
Donadon,  M. V., Almeida,  S. F. M., and de Faria,  A. R., 2002, “Stiffening Effects on the Natural Frequencies of Laminated Plates With Piezoelectric Actuators,” Composites, Part B, 33, pp. 335–342.
Kapuria,  S., and Alam,  N., 2004, “Exact Two Dimensional Piezoelasticity Solution for Buckling of Hybrid Beams and Cross-Ply Panels,” Compos. Struct., 64, pp. 1–11.
Kapuria, S., and Alam, N., 2004, “Zigzag Theory for Buckling of Hybrid Piezoelectric Beams Under Electromechanical Loads,” 46 , pp. 1–25.
Kapuria,  S., Dumir,  P. C., and Ahmed,  A., 2003, “An Efficient Coupled Layerwise Theory for Static Analysis of Piezoelectric Sandwich Beams,” Arch. Appl. Mech., 73, 147–159.


Grahic Jump Location
Geometry of the symmetric hybrid beam
Grahic Jump Location
Exact ω̄12 and error in ZIGT, TOT, and FSDT for test beam (a)
Grahic Jump Location
Exact ω̄12 and error in ZIGT, TOT, and FSDT for composite beam (b)
Grahic Jump Location
Exact ω̄12 and error in ZIGT, TOT, and FSDT for sandwich beam (c)
Grahic Jump Location
Exact ω̄32 for beams (a), (b), (c) and panel (b)
Grahic Jump Location
Effect of h/a on the error in ω1 for test beam (a)
Grahic Jump Location
Effect of h/a on the error in ω1 for composite beam (b)
Grahic Jump Location
Effect of h/a on the error in ω1 for sandwich beam (c)
Grahic Jump Location
Effect of h/a on the error in ω1 for composite panel (b)
Grahic Jump Location
Effect of h/a on the error in ω3(ε/εcr=0.5,ϕ/ϕcr=−0.25)
Grahic Jump Location
Modal distributions of ū,σ̄x,τ̄zx for beam (b)




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