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.