Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

This article aims to study the natural frequency of defective graphene sheets since the
existence of cut-outs in plates may be essential on the basis of their desired functionality.
A combination of the Aifantis theory and Kirchhoff thin plate hypothesis is used to derive
governing equations of motion. The Ritz method is employed to derive discrete equations of
motion. The molecular structural mechanics method is also employed to specify the effective
length scale parameter. In the ‘numerical results’ Section, the effects of different parameters
such as boundary conditions and diameter of the hole-to-side length ratio on the fundamental
frequency of graphene sheets are studied.