A study on graphene-reinforced magneto-electro-elastic laminated nanoplate's thermomechanical vibration behaviour based on a higher-order plate theory

Sandwich nanostructures incorporating piezoelectric and magneto-electro-elastic properties have emerged as promising candidates for next-generation smart devices and composites. Due to their exceptional design, fabrication, and energy conversion capabilities, these structures are extensively utilised as sensors and actuators in nano-electromechanical systems. Accordingly, in this article, the free vibration behaviour of a multifunctional laminated (MFL) nanoplate with piezoelectric PZT5-H and magnetostrictive CoFe₂O₄ (cobalt-ferrite) face layers and a graphene-reinforced core layer is investigated by applying a higher-order sinusoidal shear deformation theory (HSDT). In addition, two different material cases consisting of Ti6Al4V and ZrO₂ materials and two foam models, uniform and symmetric, are considered for the foam core layer. Hamilton's principle is used to obtain the plate's governing equations. Navier's solution approach is utilised to get the natural frequencies of the laminated nanoplate under thermal load and electric and magnetic fields. A parametric study is performed to determine the effects of volumetric graphene content, the foam model and its pore ratio, face/core material content, external electric and magnetic potential, and thermal load on the free vibration response of the MFL nanoplate. The obtained numerical results can be a reference point for future research on layered porous MEE structures, especially for micro/nano-sized systems.