The Influence of Surface Effects on Bending and Vibrations of Nanofilms

Abstract

Static cylindrical bending of nanofilms is considered in linear and nonlinear formulations. The frequency spectrum of bending vibrations and the parametric resonance are determined. In this case, two surface effects are taken into account. The first one is associated with different elastic properties in the surface layer and in the bulk of the material. It is manifested in stretching and bending of nanometer-thick films. The second effect is due to the difference, caused by bending, between the areas of the convex and concave surfaces subjected to gas pressure. The greater the ratio of the mean pressure to the elastic modulus of the material and the ratio of the length of the film to its thickness, the stronger this effect. The loading conditions of the end surfaces of the film are also important, as well as the strain over the film thickness under the action of the mean pressure. A positive mean pressure leads to an increase in effective stiffness, a decrease in deflection, and an increase in natural frequencies. A negative mean pressure reduces stiffness and natural frequencies. It is shown that, in this case, film bending may occur as a result of the longitudinal in stability. Oscillations of the mean pressure lead to a parametric amplification of bending vibrations. These results cannot be obtained on the basis of the classical equations of bending of plates and films.