Free vibration analysis of smart piezoelectric GPL-reinforced FGM microplates placed on Winkler–Pasternak foundation
摘要
Graphene-reinforced composites are increasingly employed as core layers in smart microplates due to their exceptional mechanical and functional properties. Although graphene or graphene platelets (GPLs) are typically used to reinforce homogeneous matrices, integrating GPLs into conventional functionally graded materials (FGMs) represents a novel approach. This study proposed a new material model comprising a GPL-reinforced FGM core with piezoelectric coating layers. The composite matrix is continuously graded through the thickness following a power-law distribution, and five distinct GPL dispersion patterns are examined. The core’s material properties are determined using the modified Halpin–Tsai model in conjunction with the rule of mixtures. Based on variants of a four-unknown refined plate theory (RPT4) combined with the modified couple stress theory (MCST), governing equations for smart GPL-reinforced FGM microplates with two piezoelectric layers resting on a Winkler–Pasternak foundation are derived. A Navier-based analytical solution is then employed to compute the natural frequencies of the piezoelectric microplate. The performance of the proposed model and the different RPT4 variants is assessed, and the influences of material parameters, piezoelectric layer thickness, length scale, and foundation parameters on the natural frequency are thoroughly investigated.