Investigating the buckling and vibration of a Mindlin rectangular nanoplate using modified couple stress theory

This paper presents the buckling and vibration characteristics of a Mindlin rectangular nanoplate with simply supported boundary conditions and Navier approach. 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. The critical buckling load values and vibration frequencies of different modes are separately solved. The governing equations are numerically solved and results are verified with literature. The effect of material length scale, length, width and thickness of the nanoplate on the buckling loads and vibration frequencies are investigated and the results are presented and discussed in details.

Keywords:

Modified couple stress theory , Mindlin nanoplate , Buckling , Vibration , Navier' s solution