Nonlocal nonlinear vibration of porous Graphene Platelets microplates under nonlinear temperature rises using modified couple stress theory based on Bézier extraction of NURBS

Abstract

This study deals with the size-dependent nonlinear vibration and dynamic responses of microplates reinforced by the porous Graphene Platelets (GPL) nanofillers under the thermal environment. The heat conduction is taken into account by the graphene platelets dispersion and porosity distribution, and the nonlinear temperature rise is assumed to be varied in thickness. To pursue the research purpose, the modified couple stress and nonlocal theories with the geometrically nonlinear analysis based on the higher-order shear strains are integrated to describe the mechanical characteristics of microplates. Three GPL distributions in conjunction with three porosity patterns dispersed along the thickness cause the nonlinear temperature profiles to vary with the relative density and porosity. The nonclassical motion equilibrium equations are established with the aid of the virtual work’s principle, the Halpin–Tsai micromechanical modeling, and the new nonlinear temperature profiles solved by heat conduction. Moreover, the improved iterative method produced into the Bézier extraction approach scrutinizes the microplate's size-dependent thermal frequency-deflection responses. Consequently, the desired mechanical properties and the structural characteristics of the GPL intact and hearted cutout microplates have been efficiently enhanced by incorporating the porosity coefficient, GPL dispersion, negative GPL thermal expansion, and length scale parameter, particularly under nonlinear temperature conditions.