bending and vibration analysis of the third-order rectangular nanoplates using the modified couple stress theory

In this paper a third-order rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress theory. the bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, and the frequencies of the nanoplate are all obtained for various plate’s dimensional ratios and material length scale to thickness ratios. the governing equations are numerically solved. the effect of material length scale, length, width and thickness of the nanoplate on the bending and vibration ratios are investigated and the results are presented and discussed in details.