Homogenization, Sandwich plate, Functionally graded plate, Deflection, Navier solution.

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This study investigates the response of small-scale length parameters and homogenization models of a simply supported nano-plate composed of functionally graded material. The natural frequency is presented for all cases, and the effect of different modes (Voigt, Reuss, LRVE, and Tamura), thickness ratio, and nonlocal parameter on the natural frequency is analyzed. The results show that the homogenization scheme is more influential in the vibrational response of FGM nanoplate with lower aspect ratios, and an increase in the small scale parameter causes a decrease in the natural frequency. To derive the governing equations and resolve them, the virtual work principle and Navier's model were employed. The accuracy of the proposed analytical model was verified by comparing the results with those obtained from other models available in the literature.