On the large deformation vibrations of Graphene platelets-reinforced composite plates located on elastic foundation: nonlinear analytical method

The nonlinear vibration analysis of a sandwich rectangular plate is presented in this study. The layers of the plate are composed of composites reinforced with graphene nanoplatelets, while the plate's core is composed of honeycomb structures. The fundamental relations of equation motions are derived using the displacement field of first-order shear deformation theory. Furthermore, geometric nonlinearity is taken into consideration by using von-Karman nonlinear strains. The Hamilton’s principle is utilized to govern the partial equations of motion. Galerkin’s technique is used to simplify the equation motions into a nonlinear motion equation. The multiple scales method is then used to solve the nonlinear motion equation. The impact of many factors, including the volume percentage and dispersion of graphene nanoplatelets along thickness axes, distinct parameters of the honeycomb core, geometric attributes, and initial conditions, on the nonlinear-to-linear frequency ratio is examined.