A new trigonometric shear deformation theory for free vibration of graphene reinforced metal-matrix nanocomposite plate submerged in fluid medium

A novel trigonometric shear deformation plate theory (TSDPT) is proposed for the vibrational characteristics of the functionally graded graphene-reinforced metal matrix nanocomposite (FG-GRMMNC) plate immersed in the fluid medium. Combining trigonometric and inverse trigonometric functions, a new shape function is presented to determine the distribution of the transverse shear strains and stresses without using any transverse shear correction factors. Using a combination of the Halpin-Tsai micromechanical model and the rule of mixtures, the properties of three distributions of GRMMNC are investigated. Aluminum serves as the matrix material, and graphene nanoplatelets are utilized as the reinforcing material. Due to the ideal and incompressible fluid medium, the influence of hydrostatic pressures and free surface waves on structures is disregarded. The governing equations are derived using the Hamilton's principle, taking into account the influences of three plate-fluid interaction models. The Galerkin's method is then utilized to determine the natural frequencies of the FG-GRMMNC plate with simply supported boundary conditions. To confirm the validity of the proposed theory, the obtained outcomes are compared with those found in the published works. On the vibrational characteristics of the nanocomposite plate, influences of material properties, distribution patterns, geometrical parameters, and fluid environments are also investigated in depth.