Influence of surface integrity on geometry and dynamics of functionally graded nanobeams

Abstract

In this study effects of surface integrity on the mechanics of functionally graded (FG) nanobeams are investigated. This study reports the changes in the geometry and dynamics of FG nanobeams because of changes in their surface textures and/or surface mechanical properties. A new model for FG nanobeams with engineering surfaces is developed. This engineering surface is considered as a different material phase with a surface texture (waviness and roughness). The initial curvatures of cantilever, simple supported, and clamped-clamped FG nanobeams due to surface residual stresses are determined. Moreover, their natural frequencies and mode shapes are derived depending on surface integrity. The initial curvatures of FG beams are obtained increasing with an increase in the slope of the surface texture and/or a decrease in the heights of the surface roughness. Moreover, it is observed that the natural frequencies of FG beams may decrease or increase due surface integrity depending on the boundary conditions. Thus, as a first prospect, the surface roughness allows the vibration energy to propagation over the beam length and hence its natural frequency decreases resulting in a zero-frequency mode. As for the other prospect, surface roughness inhibits the propagation of the vibration energy through the beam length leading to a mode localization. It is revealed that a mode localization is accompanied with an increase in the natural frequency of the nanobeam. The proposed surface integrity model for FG nanobeams is compared with Gurtin-Murdoch surface elasticity model. The results demonstrate that the surface integrity model is preferred over the former model where it accounts for, both, surface texture and surface mechanical properties effects. However, Gurtin-Murdoch model assumes smooth surfaces of nanobeams which leads to under/overestimations of their mechanics.