Free vibration analysis of graphene reinforced functionally graded nanocomposite plates in contact with quiescent bounded fluids on both sides

This paper investigates the vibrational characteristics of functionally graded porous (FGP) nanocomposite plates reinforced with graphene platelets (GPL), incorporating internal line supports, and in contact with fluids on both sides. The nanocomposite plate functions as a vertical wall, separating two rigid tanks containing quiescent, inviscid, irrotational, and incompressible fluids. Three porosity distribution types and three GPL dispersion patterns are examined. The effects of various parameters, such as GPL weight fraction and porosity coefficient, on natural frequencies are investigated, and for the first time, the effect of porosity cell type on the vibrational behavior of the nanocomposite plate is studied. Finally, the impact of fluids’ depth on the plate's natural frequencies, mode shapes, and mode order is also discussed. To achieve this, a model for the displacement field, kinetic energy, and strain energy of the nanocomposite plate accounting for both open and closed cell porosity types is developed, employing first-order shear deformation theory (FSDT). This model, in tandem with a fluid-solid interaction model that takes into account both sloshing and bulging modes of the fluids, leads to the formulation of a symmetric eigenvalue problem. Solving this problem via the Rayleigh-Ritz method leads to natural frequencies and mode shapes for the nanocomposite plate.