Abstract
Free vibration of thin functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been discussed in this chapter by using the Rayleigh-Ritz method (as stated in Chapter 3). The stress-strain relations are considered based on classical plate theory. The power-law form along thickness direction is assumed for gradation of material properties of FG elliptic plate constituents. Trial functions denoting the displacement components are expressed as simple algebraic polynomials, which can handle any classical edge support with ease. The tests of convergence of natural frequencies are summarized along with the validation in special cases. Consequently, the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies can be estimated. Moreover, 3D mode shapes for circular and elliptic FG plates with various boundary conditions at the edges are also demonstrated.
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