| Popis: |
In this paper a model is developed for the buckling and vibration analysis of a Kirchhoff rectangular nanoplate based on a modified couple stress theory. In order to consider the small scale effects, the modified couple stress theory, with one length scale parameter, is used. In modified couple stress theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. After obtaining the strain and kinetic energy, external work and substituting them in the Hamilton’s principle, the main and auxiliary equations of the nanoplate are obtained. Then, by manipulating the boundary conditions the governing equations are solved using Navier approach for buckling and vibration of the nanoplate. The dimensionless critical force under a bi-axial surface force in x and y directions and frequencies of different modes 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 buckling ratios and frequencies are investigated and the results are presented and discussed in details. |
