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Research Papers

Geometrically Nonlinear Free Vibration of Laminated Composite Plate Embedded With Piezoelectric Layers Having Uncertain Material Properties

[+] Author and Article Information
Padmanav Dash

e-mail: padmanavdash@yahoo.co.in

B. N. Singh

e-mail: bnsingh@aero.iitkgp.ernet.in
Department of Aerospace Engineering,
Indian Institute of Technology,
Kharagpur 721302, India

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 25, 2009; final manuscript received April 18, 2012; published online October 29, 2012. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 134(6), 061006 (Oct 29, 2012) (13 pages) doi:10.1115/1.4006757 History: Received July 25, 2009; Revised April 18, 2012

In this paper, the nonlinear free vibration stochastic characteristic of a smart laminated composite plate having random system properties is presented. The transverse shear effects have been included in the system equation in the frame work of higher order shear deformation theory. The analysis uses the Green-Lagrange nonlinear strain displacement relationship to model geometric nonlinearity. The direct iteration approach is used to handle deterministic geometric nonlinearity, and the perturbation approach is employed to handle the randomness in the system properties. Mean and variance of the random natural frequencies have been obtained by employing a C0 isoparametric nonlinear finite element model. Comparisons with the published results show the accuracy of the proposed procedure. A few results covering various features have been presented for a laminated composite plate with different boundary conditions.

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Figures

Grahic Jump Location
Fig. 1

Geometry of the smart laminated composite plate

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Fig. 4

Influence of SD of basic material properties on SD of the first natural frequency for a P(450/- 450/- 450/450) square laminate with E11 changing at a time for (a) SSSS, (b) CCCC, (c) CFCF, and (d) CCFF

Grahic Jump Location
Fig. 2

Influence of SD of basic material properties on SD of the first natural frequency with w′ = 0.5, 1.0, and 1.5 for P/00/900/00/P simply supported square laminate (a) with E11 changing at a time, (b) with E22 changing at a time, (c) with ν12 changing at a time, and (d) with G12 changing at a time

Grahic Jump Location
Fig. 3

Influence of SD of basic material properties on SD of the first natural frequencies with E11 changing at a time for a simply supported square plate with a/h = 10, w′ = 0.3, 0.6, 0.9, and 1.2. For lamination scheme (a) 00/900, (b) P/00/900, (c) P/00/900/P, and (d) P/00/P/00/P.

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