Free vibration analysis of quadrilateral nanoplates based on nonlocal continuum models using the Galerkin method: the effects of small scale

Free vibration analysis of quadrilateral single-layered graphene sheets (SLGS) is carried out employing nonlocal continuum mechanics. The equations of motion of the nonlocal theory are derived using the principle of virtual work. The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis. The non-dimensional natural frequencies of skew, rhombic, trapezoidal and rectangular nanoplates considering various geometrical parameters and mode numbers are obtained and for each case the effects of the small length scale are investigated.