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Research Papers

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

[+] Author and Article Information
Erasmo Carrera

Aeronautics and Space Engineering Department,  Politecnico di Torino, Torino, Italy

Fiorenzo Adolfo Fazzolari1

School of Engineering and Mathematical Sciences,  City University London, Northampton Square, London EC1V 0HB United KingdomFiorenzo.Fazzolari.1@city.ac.uk

Luciano Demasi

Department of Aerospace Engineering and Engineering Mechanics,  San Diego State University, San Diego, CA 92182-1308

1

Corresponding author.

J. Vib. Acoust 133(6), 061017 (Nov 28, 2011) (16 pages) doi:10.1115/1.4004680 History: Received November 16, 2010; Revised May 30, 2011; Accepted June 06, 2011; Published November 28, 2011; Online November 28, 2011

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carrera’s unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Multilayered plate

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Figure 2

Linear and cubic case of ESLM

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Figure 3

Linear and cubic case of ZZM

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Figure 4

Linear and cubic case of LWM

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Figure 5

Effect of the lamination angle on frequency parameter Ω=ωa2(12ρ(1-ν12ν21)/E1h2), (a/b)=1

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Figure 6

Fundamental circular frequency parameter versus lamination angle, thickness ratio a/h = 4

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Figure 7

Fundamental circular frequency parameter versus lamination angle, thickness ratio a/h = 10

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Figure 8

Fundamental circular frequency parameter versus lamination angle, thickness ratio a/h = 20

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Figure 9

Fundamental circular frequency parameter versus lamination angle, thickness ratio a/h = 100

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Figure 10

Fundamental circular frequency parameter versus thickness ratio, lamination scheme:LS4

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Figure 11

Lamination scheme (0°/90°) and anisotropic ratio E1 /E2  = 10

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Figure 12

Lamination scheme (0°/90°)4 and anisotropic ratio E1 /E2  = 10

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Figure 13

Lamination scheme (0°/90°) and LD4 model

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Figure 14

Lamination scheme (0°/90°)4 and LD4 model

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Figure 15

z/h versus displacement component ux , ESL models, m = n = 1

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Figure 16

z/h versus displacement component ux , LW models, m = n = 1

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Figure 17

z/h versus displacement component uy , ESL models, m = n = 1

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Figure 18

z/h versus displacement component uy , LW models, m = n = 1

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Figure 19

z/h versus displacement component uz , ESL models, m = n = 1

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Figure 20

z/h versus displacement component uz , LW models, m = n = 1

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