Vibration of functionally graded sandwich microplates with porous magneto-electro-elastic facings and graphene-reinforced core under thermo-fluid-structure interactions

This study explores the vibrational behavior of a functionally graded (FG) sandwich microplate subjected to coupled thermo-fluid-structure interactions. The microplate consists of porous magneto-electro-elastic (FGPMEE) facings and a porous graphene nanoplatelet-reinforced (FGPGPLRC) core. The face layers transition from barium titanate (BaTiO 3 ) to cobalt iron oxide (CoFe 2 O 4 ) following a power-law distribution and incorporate four distinct porosity patterns. Meanwhile, the core features four porosity models and four graphene nanoplatelet (GPL) dispersion schemes. To account for size-dependent dynamics and the effect of transverse shear deformation, a modified strain gradient theory (MSGT) is combined with first-order shear deformation theory (FSDT). Thermal effects are modeled through a nonlinear temperature field across the thickness, while fluid interactions are captured using forces derived from the Navier–Stokes equations. The governing equations are formulated using Hamilton’s principle and solved analytically via the Navier technique. A comprehensive parametric study examines the impact of key factors—including temperature gradients, porosity coefficients, GPL distribution patterns, applied electric voltage, magnetic potential, and length scale parameters—on the natural frequencies of the microplate.