Nonlinear free vibrations of sandwich plates with FG GPLR face sheets based on the full layerwise finite element method

Abstract

The current article is an innovative attempt to utilize the full layerwise (LW) finite element approach for investigating the nonlinear vibrations of sandwich plates with functionally graded graphene nanoplatelets (GPLs)-reinforced face sheets. The fundamental novelty of this research is the employment of the full LW theory, which provides accuracy equivalent to three-dimensional (3D) elasticity while reducing computational cost, simplifying mesh modification, and enabling faster attainment of the element stiffness matrix by maintaining the 2D structure. The uniform or functionally graded distributions of GPLs within the face sheets are considered. The effective material properties of face sheets are estimated according to the rule of mixtures and the Halpin–Tsai model. Subsequent to confirming the convergence and validity of the numerical approach and formulation, thorough parametric analyses are executed to assess the effects of various factors involving the thickness ratio of the core-to-face sheet, edge constraints, and geometric parameters, together with dispersion pattern, volume fraction, and the dimension of GPLs on the nonlinear vibration conducts of the sandwich plate. The findings demonstrate that as the core-to-face sheet thickness ratio of the sandwich plate rises, the linear and nonlinear-to-linear frequency (NTL) display opposite trends. Furthermore, the NTL ratio is not notably altered by the configuration type of the face sheets.