There has recently been a great deal of discussion on imechanica regarding the effects of surface stress on the resonant properties of nanostructures such as nanowires.  The controversy has revolved around the strain-independent part of the surface stress, which can be shown, i.e. by Gurtin et al. APL 1976, 529-530, or by Lu et al, PRB 2005, 085405, to have no effect on the resonant frequency of the nanobeam.  The reason is because in taking the moment, and differentiating the moment to get the beam equation of motion, the strain-independent part of the surface stress drops out as it is constant, while the strain-dependent (surface elastic) part survives the differentiation.

Abstract of paper recently accepted for publication in Journal of Applied Physics:

With a shallow chemical etching the roughness with spatial frequency below a critical value grows while the roughness of higher frequency decays.

http://imechanica.org/node/1312

Dear Mechanicians,

I am reading some papers on the surface effects of nano-sized elements(bars,beams, plates, films) or defects(inhomogeneities, inclusions, cavities) these days. Some researchers have studied the surface effects on the stress state around a circular hole or an elliptic hole. I wonder if there is any research work on the surface effect around a nano-sized crack. Thank you!

We present a surface Cauchy-Born approach to modeling FCC metals with nanometer scale dimensions for which surface stresses contribute significantly to the overall mechanical response. The model is based on an extension of the traditional Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augment the bulk energy.

A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).