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In this study effects of surface integrity on the mechanics of functionallygraded (FG) nanobeams are investigated. This study reports the changes in thegeometry and dynamics of FG nanobeams because of changes in their surfacetextures and/or surface mechanical properties. A new model for FG nanobeamswith engineering surfaces is developed. This engineering surface is consideredas a different material phase with a surface texture (waviness and roughness).The initial curvatures of cantilever, simple supported, and clamped-clamped FGnanobeams due to surface residual stresses are determined. Moreover, theirnatural frequencies and mode shapes are derived depending on surface integrity.The initial curvatures of FG beams are obtained increasing with an increase inthe slope of the surface texture and/or a decrease in the heights of thesurface roughness. Moreover, it is observed that the natural frequencies of FGbeams may decrease or increase due surface integrity depending on the boundaryconditions. Thus, as a first prospect, the surface roughness allows thevibration energy to propagation over the beam length and hence its naturalfrequency decreases resulting in a zero-frequency mode. As for the otherprospect, surface roughness inhibits the propagation of the vibration energythrough the beam length leading to a mode localization. It is revealed that amode localization is accompanied with an increase in the natural frequency ofthe nanobeam. The proposed surface integrity model for FG nanobeams is comparedwith Gurtin-Murdoch surface elasticity model. The results demonstrate that thesurface integrity model is preferred over the former model where it accountsfor, both, surface texture and surface mechanical properties effects. However,Gurtin-Murdoch model assumes smooth surfaces of nanobeams which leads tounder/overestimations of their mechanics.

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