How does porosity affect the free vibration of single-layered graphene sheets?

This paper aims to investigate the influence of porosity and length size on the free vibration of single-layered graphene sheets (SLGSs). Frequency analysis is performed using a finite element based molecular structural mechanics (MSM) approach mimicking the SLGSs as frame-like structures constructed out of the beam elements. Defining a porous unit cell, 320 SLGSs with different arrangements and values of porosities and various length sizes ranging from 4 to 32 nm are considered. Results reveal that increasing porosity as well as length size both decrease the natural frequencies of SLGSs, significantly. To improve the applicability of the results, a nonlocal small scale parameter introduced by the analytical solutions for vibration of nanoplates in the literature is calibrated in such a way that the obtained frequencies by MSM match the analytical solutions based on the nonlocal theory of elasticity. Both neural network and genetic programming processes are successfully implemented for the calibration. The proposed calibrated parameter can be easily applied to evaluate the natural frequencies of SLGSs for certain values of porosities and length sizes.