Based on exact position of neutral surface, vibrational behavior of smart nanoplates made of magneto-electro-elastic functionally graded materials is examined by implementing a Galerkin method for the first time. Magneto-electro-elastic properties of nanoplate vary in transverse direction via power-law model. The nonlocal governing equations of functionally graded plate under magneto-electrical field are formulated through Hamilton’s principle and nonlocal elasticity theory based on a four-variable refined plate theory, which avoids the use of shear correction factors by capturing shear deformation influences. Importance of various parameters including magnetic potential, electric voltage, various boundary conditions, nonlocality, material distribution, and plate thickness on natural frequencies of the magneto-electro-elastic functionally graded nanoplate are explored. It is elucidated that these parameters play significant roles on the dynamic behavior of magneto-electro-elastic functionally graded nanoplates.
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