The natural frequency analysis of FG-GNPR nanoplates under different boundary conditions

Because of their remarkable mechanical qualities, nano-composites—components that are 100 nanometers or smaller—have started to be used in modern engineering. Among these are graphene nanoplatelets (GNPs), which offer a number of advantages over other nanomaterials, including low gas permeability, thermal conductivity, and electrical conductivity. The present study presents natural frequency analysis of functionally graded graphene nanoplatelet reinforced (FG-GNPR) nanoplates. For this context, a refined four-variable plate theory (RPT) is utilized considering several boundary conditions. Eringen's nonlocal elasticity theory is employed to take account of the size-dependent effect of nanoplates. The distributions of GNPs in the polymer matrix are considered to be uniform and non-uniform patterns. Hamilton's principle is employed to solve the governing equations of FG-GNPR nanoplate. The obtained results are then validated with benchmark reulsts of available in the literature. Comprehensive parametrical investigations are carried out, and the effects of nonlocal parameter, weight fraction, and the boundary conditions on the free vibration response of FG-GNPR polymer composite nanoplates are examined in detail. For design engineers, the study offers insightful information on how various factors and boundary conditions affect the natural frequency of plates.