Size dependent vibration of curved nanobeams and rings including surface energies

In this article, explicit solution is presented for size and geometry dependent free vibration of curved nanostructures with consideration of surface properties. Additional surface elasticity, surface residual stress and also surface mass density are included in the study to generalize the existing classical theories. Considering the general presentation of the problem and regardless of the boundary conditions, the deviations of actual dynamic characteristics from classical theories for various geometries are found as new results. The modified natural frequencies of the structure are thus obtained and presented as normalized with respect to their corresponding conventional values.

Research HighlightsThe following options are the characteristics and merits of this research paper: ►Explicit solution is presented for vibration of a curved nanoelement including surface effects. ►Size dependent dynamic behavior of such structures is illustrated under the effect of surface properties. ►Using equilibrium equations, the classical theories are modified efficiently to include the surface energy parameters. ►Equivalent geometries of curved beam regardless to the boundary conditions are introduced as a novel result for both with and without surface effect considerations. ►It is concluded that for the fundamental vibration mode and for thickness higher than 20 nm, the surface effects can be ignored with no significant error in the results.