Electro-thermal vibration of graphene platelets reinforced functionally graded piezoelectric microplates under different boundary conditions

The paper presents, for the first time, the electro-thermal vibration behavior of novel graphene platelet (GPL)reinforced functionally graded piezoelectric material (FGPM) microplates under various boundary conditions. The matrix material consists of two piezoelectric materials, with properties varying continuously across the thickness according to a power-law model. The FGPM matrix is reinforced by GPLs in five distribution patterns: symmetric-1 (G1), symmetric-2 (G2), asymmetric-1 (G3), asymmetric-2 (G4), and uniform (G5). The smart microplate model is developed using the four-variable refined plate theory (RPT-4) and modified couple stress theory. Its accuracy and reliability are validated through the Rayleigh-Ritz method, showing excellent agreement with benchmark results. A comprehensive investigation is conducted into the effects of GPL reinforcement, power-law index, boundary conditions, size dependency, side-to-thickness ratio, applied voltage, and temperature rise on the fundamental frequency of the smart microplates.