Exact analytical solution for free vibration of functionally graded thin annular sector plates resting on elastic foundation

This article introduces an exact analytical method for free vibration analysis of functionally graded (FG) thin annular sector plates resting on Winkler and Pasternak elastic foundations. The annular sector plate has simply supported radial edges and arbitrary boundary conditions along the circular...

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Bibliographic Details
Published in:Journal of vibration and control 2012-02, Vol.18 (2), p.246-267
Main Authors: Baferani, A Hasani, Saidi, AR, Jomehzadeh, E
Format: Article
Language:English
Subjects:
Annular
Boundary conditions
Eigenvalues
Equations of motion
Foundations
Free vibration
Functionally gradient materials
Materials elasticity
Mathematical analysis
Numerical analysis
Plates
Vibration analysis
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Summary:This article introduces an exact analytical method for free vibration analysis of functionally graded (FG) thin annular sector plates resting on Winkler and Pasternak elastic foundations. The annular sector plate has simply supported radial edges and arbitrary boundary conditions along the circular edges. Based on the displacement field of Kirchhoff plate theory, the governing equations of motion are obtained considering the in-plane displacements and rotary inertia. Using a set of functions, the three coupled governing equations of motion are converted into two decoupled equations. By applying the boundary conditions at inner and outer radii, an eigenvalue problem for finding the natural frequencies is obtained. The nine distinct cases are considered involve all possible combinations of boundary conditions along the circular edges. Accurate non-dimensional frequency is presented for over a wide range of sector angles, some inner to outer radii (aspect ratio) and different powers of functionally graded material. Accurate natural frequencies of FG annular sector plates resting on elastic foundations are presented for the first time and can be used as reference values for numerical analyses.
ISSN:1077-5463
1741-2986
DOI:10.1177/1077546311402530