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Structural Engineering and Mechanics Volume 53, Number 2, January25 2015 , pages 337-354 DOI: https://doi.org/10.12989/sem.2015.53.2.337 |
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Free vibration of functionally graded thin elliptic plates with various edge supports |
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K.K. Pradhan, S. Chakraverty
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| Abstract | ||
| In this article, free vibration of functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been investigated. Literature review reveals no study has been performed based on functionally graded elliptic plates till date. The mechanical kinematic relations are considered based on classical plate theory. Rayleigh-Ritz technique is used to obtain the generalized eigenvalue problem. The material properties of the FG plate are assumed to vary along thickness direction of the constituents according to power-law form. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any edge support. The objective is to study the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. A comparison study is carried out with existing literature for validation in special cases. Three-dimensional mode shapes for circular and elliptic FG plates are also presented with various boundary conditions at the edges. | ||
| Key Words | ||
| vibration; elliptic functionally graded plate; Rayleigh-Ritz method; classical plate theory; mode shapes | ||
| Address | ||
| K.K. Pradhan, S. Chakraverty: Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India | ||