Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates

The small- and large-amplitude vibrations are presented for a functionally graded rectangular plate resting on a two-parameter (Pasternak-type) elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt (V) model and Mori-Tanaka (M-T) model, are considered. The motion equations are based on a higher order shear deformation plate theory that includes plate-foundation interaction. The thermal effects are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The accuracy of Voigt and Mori-Tanaka models for the vibration analysis of FGM plates is investigated. The comparison studies reveal that the difference between these two models is much less compared to the difference caused by different solution methodologies and plate theories. The results show that the difference of the fundamental frequencies between M-T and V solutions is very small, and the difference of the nonlinear to linear frequency ratios between M-T and V solutions may be negligible.