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Design and Analysis

Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates on Elastic Foundations via State-Space Based Differential Quadrature Method

[+] Author and Article Information
A. Jodaei1

Young Researchers Club, Science and Research Branch,  Islamic Azad University, Tehran 14778-93855, Irana_jodaei@yahoo.com

M. H. Yas

Mechanical Engineering Department,  Razi University, Kermanshah 67149-67346, Iranyas@razi.ac.ir

1

Corresponding author.

J. Pressure Vessel Technol 134(3), 031208 (May 18, 2012) (17 pages) doi:10.1115/1.4005939 History: Received May 21, 2011; Revised November 21, 2011; Published May 17, 2012; Online May 18, 2012

In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry of the FGM annular plate on elastic foundation

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Figure 2

Variation of the first non-dimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2m,h=0.1,λ=1)

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Figure 3

Variation of the first nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 4

Variation of the second nondimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 5

Variation of the second nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 6

Variation of the third nondimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 7

Variation of the third nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 8

Variation of the first nondimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 9

Variation of the first nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 10

Variation of the second nondimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 11

Variation of the second nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 12

Variation of the third nondimensional natural frequency parameter of c-c annular FG plate on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 13

Variation of the third nondimensional natural frequency parameter of s-c annular FG plates on elastic foundation versus shearing layer elastic coefficient for different Winkler elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

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Figure 14

Variation of nondimensional natural frequency parameter versus large values of Kg for different thicknesses (a=1 m,b=0.2 m,λ=1,m=1,Kw=0)

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Figure 15

Variation of the first nondimensional natural frequency parameter of s-s annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 16

Variation of the second nondimensional natural frequency parameter of s-s annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

Grahic Jump Location
Figure 17

Variation of the third nondimensional natural frequency parameter of s-s annular FG plates on elastic foundation versus Winkler elastic coefficient for different shearing layer elastic coefficient (a=1 m,b=0.2 m,h=0.1,λ=1)

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Figure 18

Variation of the first nondimensional natural frequency parameter versus λ for different Winkler and shearing layer elastic coefficients and different boundary conditions (a=1 m,b=0.2 m,h=0.1)

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Figure 19

Variation of the second nondimensional natural frequency parameter versus λ for different Winkler and shearing layer elastic coefficients and different boundary conditions (a=1 m,b=0.2 m,h=0.1)

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Figure 20

Variation of the third nondimensional natural frequency parameter versus λ for different Winkler and shearing layer elastic coefficients and different boundary conditions (a=1 m,b=0.2 m,h=0.1)

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