Bending, Buckling and Vibration analysis of third order shear deformation nanoplate based on modified couple stress theory

Abstract

In this paper a third order shear deformation rectangular nanoplate with simply supported boundary conditions is developed for bending, buckling and vibration analysis. In order to consider the small-scale effects, the modified couple stress theory, with one length scale parameter, is used. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, the dimensionless critical force under a uniaxial surface force in x direction and dimensionless frequencies 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, buckling and vibration ratios are investigated and the results are presented and discussed in detail.